Pub Date : 2022-09-10DOI: 10.18187/pjsor.v18i3.4180
G. Hamedani, I. Ghosh, A. Saghir
We would like to point out that the formula for the cumulative distribution given in Coelho-Barros et al. (2017) and a similar version of it given in Usman et al. (2021) are not cumulative distribution functions as these functions do not satisfy the one or more necessary and sufficient conditions for a function to be a cumulative distribution function. We would also like to mention that formulas for the cumulative distribution functions of product and ratio of two independent Pareto and Exponential random variables given by Obeid and Kadry (2022) are not cumulative distribution functions either. We do not believe that these formulas can be fixed to be cumulative distribution functions. In this short article, we provide mathematical justification in support of these claims.
{"title":"Remarks on the Papers by Coelho-Barros et al. (2017), Usman et al. (2021) and Obeid and Kadry (2022)","authors":"G. Hamedani, I. Ghosh, A. Saghir","doi":"10.18187/pjsor.v18i3.4180","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.4180","url":null,"abstract":"We would like to point out that the formula for the cumulative distribution given in Coelho-Barros et al. (2017) and a similar version of it given in Usman et al. (2021) are not cumulative distribution functions as these functions do not satisfy the one or more necessary and sufficient conditions for a function to be a cumulative distribution function. We would also like to mention that formulas for the cumulative distribution functions of product and ratio of two independent Pareto and Exponential random variables given by Obeid and Kadry (2022) are not cumulative distribution functions either. We do not believe that these formulas can be fixed to be cumulative distribution functions. In this short article, we provide mathematical justification in support of these claims.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45902129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.18187/pjsor.v18i3.4007
A. Hanandeh, Omar M. Eidous
Due to the widespread applicability and use of the normal distribution, a need has arisen to approximate its cumulative distribution function (cdf). In this article, five new simple approximations to the standard normal cdf are developed. In order to assess the accuracy of the proposed approximations, both maximum absolute error and mean absolute error were used. The maximum absolute errors of the proposed approximations lie between 0.00095 and 0.00946, which is highly accurate if compared to the existing simple approximations and quite sufficient for many real-life applications. Even though simple approximations may not as accurate as complicated ones, they are, though, fairly good when judged vis-a-vis their simplicity.
{"title":"Some improvements for existing simple Approximations of the Normal Distribution Function","authors":"A. Hanandeh, Omar M. Eidous","doi":"10.18187/pjsor.v18i3.4007","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.4007","url":null,"abstract":"Due to the widespread applicability and use of the normal distribution, a need has arisen to approximate its cumulative distribution function (cdf). In this article, five new simple approximations to the standard normal cdf are developed. In order to assess the accuracy of the proposed approximations, both maximum absolute error and mean absolute error were used. The maximum absolute errors of the proposed approximations lie between 0.00095 and 0.00946, which is highly accurate if compared to the existing simple approximations and quite sufficient for many real-life applications. Even though simple approximations may not as accurate as complicated ones, they are, though, fairly good when judged vis-a-vis their simplicity.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48277085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.18187/pjsor.v18i3.3982
N. S. Zulkipli, S. Z. Satari, W. N. S. Wan Yusoff
The procedure of outliers detection in univariate circular data can be developed using clustering algorithm. In clustering, it is necessary to calculate the similarity measure in order to cluster the observations into their own group. The similarity measure in circular data can be determined by calculating circular distance between each point of angular observation. In this paper, clustering-based procedure for outlier detection in univariate circular biological data with different similarity distance measures will be developed and the performance will be investigated. Three different circular similarity distance measures are used for the outliers detection procedure using single-linkage clustering algorithm. However, there are two similarity measures namely Satari distance and Di distance that are found to have similarity in formula for univariate circular data. The aim of this study is to develop and demonstrate the effectiveness of proposed clustering-based procedure with different similarity distance measure in detecting outliers. Therefore, in this study the circular similarity distance of SL-Satari/Di and another similarity measure namely SL-Chang will be compared at certain cutting rule. It is found that clustering-based procedure using single-linkage algorithm with different similarity distances are applicable and promising approach for outlier detection in univariate circular data, particularly for biological data. The result also found that at a certain condition of data, the SL-Satari/Di distance seems to overperform the performance of SL-Chang distance.
{"title":"The Effect of Different Similarity Distance Measures in Detecting Outliers Using Single-Linkage Clustering Algorithm for Univariate Circular Biological Data","authors":"N. S. Zulkipli, S. Z. Satari, W. N. S. Wan Yusoff","doi":"10.18187/pjsor.v18i3.3982","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.3982","url":null,"abstract":"The procedure of outliers detection in univariate circular data can be developed using clustering algorithm. In clustering, it is necessary to calculate the similarity measure in order to cluster the observations into their own group. The similarity measure in circular data can be determined by calculating circular distance between each point of angular observation. In this paper, clustering-based procedure for outlier detection in univariate circular biological data with different similarity distance measures will be developed and the performance will be investigated. Three different circular similarity distance measures are used for the outliers detection procedure using single-linkage clustering algorithm. However, there are two similarity measures namely Satari distance and Di distance that are found to have similarity in formula for univariate circular data. The aim of this study is to develop and demonstrate the effectiveness of proposed clustering-based procedure with different similarity distance measure in detecting outliers. Therefore, in this study the circular similarity distance of SL-Satari/Di and another similarity measure namely SL-Chang will be compared at certain cutting rule. It is found that clustering-based procedure using single-linkage algorithm with different similarity distances are applicable and promising approach for outlier detection in univariate circular data, particularly for biological data. The result also found that at a certain condition of data, the SL-Satari/Di distance seems to overperform the performance of SL-Chang distance.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43942908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.18187/pjsor.v18i3.4096
F. Yanuar, A. Zetra
Originating from Wuhan, China, COVID-19 is spreading rapidly throughout the world. The epidemiological model is required to provide evidence for public health policymakers to reduce the spread of COVID-19. Health behaviour is assumed could reduce the spread of this virus. This study purposes to construct an acceptable model of health behaviour. To achieve this goal, a Bayesian structural equation modelling (SEM) is implemented. This current study is also purposed to evaluate the performance of Bayesian SEM, including the sensitivity, adequacy, and the acceptability of parameters estimated with the result that the acceptable model is obtained. The sensitivity of the Bayesian SEM estimator is evaluated by choosing several types of prior and the model results are compared. The adequacy of the Bayesian SEM estimate is checked by doing the convergence test of the corresponding model parameters. The acceptability of the Bayesian approach and its associated algorithm in recovering the true parameters are monitored by the Bootstrap simulation study. The Bayesian SEM applies the Gibbs sample approach in estimating model parameters. This method is applied to the primary data gathered from an online survey from March to May 2020 during COVID-19 to individuals living in West Sumatera, Indonesia. It is found that health motivation is significantly related to health behaviour. Whereas socio-demographic and perceived susceptibility has no significant effect on health behaviour.
{"title":"The Performance of Bayesian Analysis in Structural Equation Modelling to Construct The Health Behaviour During Pandemic COVID-19","authors":"F. Yanuar, A. Zetra","doi":"10.18187/pjsor.v18i3.4096","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.4096","url":null,"abstract":"Originating from Wuhan, China, COVID-19 is spreading rapidly throughout the world. The epidemiological model is required to provide evidence for public health policymakers to reduce the spread of COVID-19. Health behaviour is assumed could reduce the spread of this virus. This study purposes to construct an acceptable model of health behaviour. To achieve this goal, a Bayesian structural equation modelling (SEM) is implemented. This current study is also purposed to evaluate the performance of Bayesian SEM, including the sensitivity, adequacy, and the acceptability of parameters estimated with the result that the acceptable model is obtained. The sensitivity of the Bayesian SEM estimator is evaluated by choosing several types of prior and the model results are compared. The adequacy of the Bayesian SEM estimate is checked by doing the convergence test of the corresponding model parameters. The acceptability of the Bayesian approach and its associated algorithm in recovering the true parameters are monitored by the Bootstrap simulation study. The Bayesian SEM applies the Gibbs sample approach in estimating model parameters. This method is applied to the primary data gathered from an online survey from March to May 2020 during COVID-19 to individuals living in West Sumatera, Indonesia. It is found that health motivation is significantly related to health behaviour. Whereas socio-demographic and perceived susceptibility has no significant effect on health behaviour. ","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49663589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.18187/pjsor.v18i3.3915
Yuni Kurniawati, M. Muhajir
Gold is a precious metal often used for investment, due to its cash-in ease and yearly value increase. This indicates that price forecasting is used to determine the prospect of future gold prices. Strong gold price forecasting is highly desired by investors to make decisions. That is why technical indicators are very important used for forecasting. By using technical indicators the information obtained can be more informative than using pure gold prices. One of the commonly used methods is Backpropagation (BP). BP has been shown to have good performance in dealing with nonlinear problems. However, due to the random determination of the parameters of neurons in the hidden layer BP requires a number of neurons in the hidden layer to get optimal results. Therefore, this study aims to analyze the optimization of Backpropagation (BP) through the Harmony Search (HS) algorithm by evaluating the use of relevant technical indicators for forecasting gold prices. In the HS-BP model, this method is used to determine input variables and neurons in the hidden layer. HS with the principle of musicians with the aim of finding the best harmony. This technique is used based on the results of the fitness function. In this research, the fitness function used is Mean Square Error (MSE). HS aims to optimize BP in such a way that the forecasting system provides the lowest MSE and improves the forecasting performance of gold prices. Based on this research, the input variables used are Moving Average, Relative Strength Index, and Bollinger Bands. Next, the selected variables and neurons are applied to the BP algorithm. Where the implementation uses gold closing price data for January 2020-2021. The results showed that the proposed method has better results in forecasting accuracy and convergence error. HS-BP provides a better level of gold price forecasting than the regular BP model.
{"title":"Optimization of Backpropagation Using Harmony Search for Gold Price Forecasting","authors":"Yuni Kurniawati, M. Muhajir","doi":"10.18187/pjsor.v18i3.3915","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.3915","url":null,"abstract":"Gold is a precious metal often used for investment, due to its cash-in ease and yearly value increase. This indicates that price forecasting is used to determine the prospect of future gold prices. Strong gold price forecasting is highly desired by investors to make decisions. That is why technical indicators are very important used for forecasting. By using technical indicators the information obtained can be more informative than using pure gold prices. One of the commonly used methods is Backpropagation (BP). BP has been shown to have good performance in dealing with nonlinear problems. However, due to the random determination of the parameters of neurons in the hidden layer BP requires a number of neurons in the hidden layer to get optimal results. Therefore, this study aims to analyze the optimization of Backpropagation (BP) through the Harmony Search (HS) algorithm by evaluating the use of relevant technical indicators for forecasting gold prices. In the HS-BP model, this method is used to determine input variables and neurons in the hidden layer. HS with the principle of musicians with the aim of finding the best harmony. This technique is used based on the results of the fitness function. In this research, the fitness function used is Mean Square Error (MSE). HS aims to optimize BP in such a way that the forecasting system provides the lowest MSE and improves the forecasting performance of gold prices. Based on this research, the input variables used are Moving Average, Relative Strength Index, and Bollinger Bands. Next, the selected variables and neurons are applied to the BP algorithm. Where the implementation uses gold closing price data for January 2020-2021. The results showed that the proposed method has better results in forecasting accuracy and convergence error. HS-BP provides a better level of gold price forecasting than the regular BP model.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49102686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.18187/pjsor.v18i3.3652
M. Hamed, G. Cordeiro, H. Yousof
Analyzing the future values of anticipated claims is essential in order for insurance companies to avoid major losses caused by prospective future claims. This study proposes a novel three-parameter compound Lomax extension. The new density can be "monotonically declining", "symmetric", "bimodal-asymmetric", "asymmetric with right tail", "asymmetric with wide peak" or "asymmetric with left tail". The new hazard rate can take the following shapes: "J-shape", "bathtub (U-shape)", "upside down-increasing", "decreasing-constant", and "upside down-increasing". We use some common copulas, including the Farlie-Gumbel-Morgenstern copula, the Clayton copula, the modified Farlie-Gumbel-Morgenstern copula, Renyi's copula and Ali-Mikhail-Haq copula to present some new bivariate quasi-Poisson generalized Weibull Lomax distributions for the bivariate mathematical modelling. Relevant mathematical properties are determined, including mean waiting time, mean deviation, raw and incomplete moments, residual life moments, and moments of the reversed residual life. Two actual data sets are examined to demonstrate the unique Lomax extension's usefulness. The new model provides the lowest statistic testing based on two real data sets. The risk exposure under insurance claims data is characterized using five important risk indicators: value-at-risk, tail variance, tail-value-at-risk, tail mean-variance, and mean excess loss function. For the new model, these risk indicators are calculated. In accordance with five separate risk indicators, the insurance claims data are employed in risk analysis. We choose to focus on examining these data under five primary risk indicators since they have a straightforward tail to the left and only one peak. All risk indicators under the insurance claims data are addressed for numerical and graphical risk assessment and analysis.
{"title":"A New Compound Lomax Model: Properties, Copulas, Modeling and Risk Analysis Utilizing the Negatively Skewed Insurance Claims Data","authors":"M. Hamed, G. Cordeiro, H. Yousof","doi":"10.18187/pjsor.v18i3.3652","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.3652","url":null,"abstract":"Analyzing the future values of anticipated claims is essential in order for insurance companies to avoid major losses caused by prospective future claims. This study proposes a novel three-parameter compound Lomax extension. The new density can be \"monotonically declining\", \"symmetric\", \"bimodal-asymmetric\", \"asymmetric with right tail\", \"asymmetric with wide peak\" or \"asymmetric with left tail\". The new hazard rate can take the following shapes: \"J-shape\", \"bathtub (U-shape)\", \"upside down-increasing\", \"decreasing-constant\", and \"upside down-increasing\". We use some common copulas, including the Farlie-Gumbel-Morgenstern copula, the Clayton copula, the modified Farlie-Gumbel-Morgenstern copula, Renyi's copula and Ali-Mikhail-Haq copula to present some new bivariate quasi-Poisson generalized Weibull Lomax distributions for the bivariate mathematical modelling. Relevant mathematical properties are determined, including mean waiting time, mean deviation, raw and incomplete moments, residual life moments, and moments of the reversed residual life. Two actual data sets are examined to demonstrate the unique Lomax extension's usefulness. The new model provides the lowest statistic testing based on two real data sets. The risk exposure under insurance claims data is characterized using five important risk indicators: value-at-risk, tail variance, tail-value-at-risk, tail mean-variance, and mean excess loss function. For the new model, these risk indicators are calculated. In accordance with five separate risk indicators, the insurance claims data are employed in risk analysis. We choose to focus on examining these data under five primary risk indicators since they have a straightforward tail to the left and only one peak. All risk indicators under the insurance claims data are addressed for numerical and graphical risk assessment and analysis.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47986311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.18187/pjsor.v18i3.3420
M. Ibrahim, G. Hamedani, Nadeem Shafique Butt, H. Yousof
A new three-parameter Nadarajah Haghighi model is introduced and studied. The new density has various shapes such as the right skewed, left skewed and symmetric and its corresponding hazard rate shapes can be increasing, decreasing, bathtub, upside down and constant. Characterization results are obtained based on two truncated moments and in terms of the hazard function. Validation via a modified chi-squared goodness-of-fit test is presented under the new model. A simple type Copula based construction is employed in deriving many bivariate and multivariate type distributions. The potentiality uncensored and censored real data sets. We constructed a modified Nikulin-Rao-Robson chi-square goodness-of-fit type test for the new model. This modi…ed chi-square test takes into account both unknown parameters and censorship. Validation in case of right censoring and all the elements constituting the test criteria. The censored aluminum reduction cells data is analyzed for validation.
{"title":"Expanding the Nadarajah Haghighi Model: Copula, Censored and Uncensored Validation, Characterizations and Applications","authors":"M. Ibrahim, G. Hamedani, Nadeem Shafique Butt, H. Yousof","doi":"10.18187/pjsor.v18i3.3420","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.3420","url":null,"abstract":"A new three-parameter Nadarajah Haghighi model is introduced and studied. The new density has various shapes such as the right skewed, left skewed and symmetric and its corresponding hazard rate shapes can be increasing, decreasing, bathtub, upside down and constant. Characterization results are obtained based on two truncated moments and in terms of the hazard function. Validation via a modified chi-squared goodness-of-fit test is presented under the new model. A simple type Copula based construction is employed in deriving many bivariate and multivariate type distributions. The potentiality uncensored and censored real data sets. We constructed a modified Nikulin-Rao-Robson chi-square goodness-of-fit type test for the new model. This modi…ed chi-square test takes into account both unknown parameters and censorship. Validation in case of right censoring and all the elements constituting the test criteria. The censored aluminum reduction cells data is analyzed for validation.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46522058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-07DOI: 10.18187/pjsor.v18i3.3883
Seema Chettri, Bhanita Das, Imliyangba Imliyangba, P. Hazarika
In this paper, we proposed a new generalized family of distribution namely new alpha power Exponential (NAPE) distribution based on the new alpha power transformation (NAPT) method by Elbatal et al. (2019). Various statistical properties of the proposed distribution are obtained including moment, incomplete moment, conditional moment, probability weighted moments (PWMs), quantile function, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics. The percentage point of NAPE distribution for some specific values of the parameters is also obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters of NAPE distribution. A simulation study has been performed to evaluate and execute the behavior of the estimated parameters for mean square errors (MSEs) and bias. Finally, the efficiency and flexibility of the new proposed model are illustrated by analyzing three real-life data sets.
本文基于Elbatal et al.(2019)的new alpha power transformation (NAPT)方法，提出了一种新的广义分布族，即new alpha power Exponential (NAPE)分布。得到了该分布的各种统计性质，包括矩、不完全矩、条件矩、概率加权矩、分位数函数、残差和反残差寿命函数、应力-强度参数、熵和阶统计量。还得到了一些具体参数值的NAPE分布的百分比。本文采用极大似然估计(MLE)方法对NAPE分布参数进行估计。进行了模拟研究，以评估和执行均方误差(MSEs)和偏差估计参数的行为。最后，通过对三个实际数据集的分析，说明了该模型的有效性和灵活性。
{"title":"A Generalized Form of Power Transformation on Exponential Family of Distribution with Properties and Application","authors":"Seema Chettri, Bhanita Das, Imliyangba Imliyangba, P. Hazarika","doi":"10.18187/pjsor.v18i3.3883","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.3883","url":null,"abstract":"In this paper, we proposed a new generalized family of distribution namely new alpha power Exponential (NAPE) distribution based on the new alpha power transformation (NAPT) method by Elbatal et al. (2019). Various statistical properties of the proposed distribution are obtained including moment, incomplete moment, conditional moment, probability weighted moments (PWMs), quantile function, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics. The percentage point of NAPE distribution for some specific values of the parameters is also obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters of NAPE distribution. A simulation study has been performed to evaluate and execute the behavior of the estimated parameters for mean square errors (MSEs) and bias. Finally, the efficiency and flexibility of the new proposed model are illustrated by analyzing three real-life data sets.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47368497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-07DOI: 10.18187/pjsor.v18i3.3676
D. Lestari, Raymond Tanujaya, Rahmat Al Kafi, S. Devila
In most cases, loss in non-life insurance is calculated based on claim severity and frequency and an assumption of independence. However, in some cases, claim severity depends upon the claim frequency. This paper presents the derivation of aggregate loss calculation by modeling claim severity and frequency as the assumption of independence is eliminated. The authors modeled average claim severity using claim frequency as the covariate to induce the dependence among them. For that purpose, we use the generalized linear model. After doing parameters estimation, we will obtain the calculated loss.
{"title":"Generalized Linear Models for Loss Calculation in General Insurance","authors":"D. Lestari, Raymond Tanujaya, Rahmat Al Kafi, S. Devila","doi":"10.18187/pjsor.v18i3.3676","DOIUrl":"https://doi.org/10.18187/pjsor.v18i3.3676","url":null,"abstract":"In most cases, loss in non-life insurance is calculated based on claim severity and frequency and an assumption of independence. However, in some cases, claim severity depends upon the claim frequency. This paper presents the derivation of aggregate loss calculation by modeling claim severity and frequency as the assumption of independence is eliminated. The authors modeled average claim severity using claim frequency as the covariate to induce the dependence among them. For that purpose, we use the generalized linear model. After doing parameters estimation, we will obtain the calculated loss.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46707497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-03DOI: 10.18187/pjsor.v18i2.4043
R. Roozegar, Getachew Tekle, G. Hamedani
The researchers in applied statistics are recently highly motivated to introduce new generalizations of distributions due to the limitations of the classical univariate distributions. In this study, we propose a new family called new generalized-X family of distributions. A special sub-model called new generalized-Weibull distribution is studied in detail. Some basic statistical properties are discussed in depth. The performance of the new proposed model is assessed graphically and numerically. It is compared with the five well-known competing models. The proposed model is the best in its performance based on the model adequacy and discrimination techniques. The analysis is done for the real data and the maximum likelihood estimation technique is used for the estimation of the model parameters. Furthermore, a simulation study is conducted to evaluate the performance of the maximum likelihood estimators. Additionally, we discuss a mixture of random effect models which are capable of dealing with the overdispersion and correlation in the data. The models are compared for their best fit of the data with these important features. The graphical and model comparison methods implied a good improvement in the combined model.
{"title":"A New Generalized-X Family of Distributions: Applications, Characterization and a Mixture of Random Effect Models","authors":"R. Roozegar, Getachew Tekle, G. Hamedani","doi":"10.18187/pjsor.v18i2.4043","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.4043","url":null,"abstract":"The researchers in applied statistics are recently highly motivated to introduce new generalizations of distributions due to the limitations of the classical univariate distributions. In this study, we propose a new family called new generalized-X family of distributions. A special sub-model called new generalized-Weibull distribution is studied in detail. Some basic statistical properties are discussed in depth. The performance of the new proposed model is assessed graphically and numerically. It is compared with the five well-known competing models. The proposed model is the best in its performance based on the model adequacy and discrimination techniques. The analysis is done for the real data and the maximum likelihood estimation technique is used for the estimation of the model parameters. Furthermore, a simulation study is conducted to evaluate the performance of the maximum likelihood estimators. Additionally, we discuss a mixture of random effect models which are capable of dealing with the overdispersion and correlation in the data. The models are compared for their best fit of the data with these important features. The graphical and model comparison methods implied a good improvement in the combined model.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41766585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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