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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
Pub Date : 2022-06-02DOI: 10.18187/pjsor.v18i2.4049
Moustafa Salem, Mohamed G. Khalil
Support Vector Regression (SVR) formulates is an optimization problem to learn a regression function that maps from input predictor variables to output observed response values. The SVR is useful because it balances model complexity and prediction error, and it has good performance for handling high-dimensional data. In this paper, we use the SVR model to improve the principal component analysis and the factor analysis methods. Simulation experiments are performed to assessment the new method. Some useful applications to real data sets are presented for comparing the competitive SVR models. It is noted that with increasing sample size, the -SVR type under the principal component analysis is the best model. However, under the small sample sizes the SVR type under the factor analysis provided adequate results.
{"title":"The Support Vector Regression Model: A new Improvement for some Data Reduction Methods with Application","authors":"Moustafa Salem, Mohamed G. Khalil","doi":"10.18187/pjsor.v18i2.4049","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.4049","url":null,"abstract":"Support Vector Regression (SVR) formulates is an optimization problem to learn a regression function that maps from input predictor variables to output observed response values. The SVR is useful because it balances model complexity and prediction error, and it has good performance for handling high-dimensional data. In this paper, we use the SVR model to improve the principal component analysis and the factor analysis methods. Simulation experiments are performed to assessment the new method. Some useful applications to real data sets are presented for comparing the competitive SVR models. It is noted that with increasing sample size, the -SVR type under the principal component analysis is the best model. However, under the small sample sizes the SVR type under the factor analysis provided adequate results.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45757832","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 : 2022-06-02DOI: 10.18187/pjsor.v18i2.3938
Mohamed Aboraya, M. M. Ali, Haitham M. Yousof, Mohamed ibrahim Mohamed
In this work, we introduced a new three-parameter Nadarajah-Haghighi model. We derived explicit expressions for some of it statistical properties. The Farlie Gumbel Morgenstern, modified Farlie Gumbel Morgenstern, Clayton, Renyi and Ali-Mikhail-Haq copulas are used for deriving some bivariate type extensions. We consider maximum likelihood, Cramér-von-Mises, ordinary least squares, whighted least squares, Anderson Darling, right tail Anderson Darling and left tail Anderson Darling estimation procedures to estimate the unknown model parameters. Simulation study for comparing estimation methods is performed. An application for comparing methods as also presented. The maximum likelihood estimation method is the best method. However, the other methods performed well. Another application for comparing the competitive models is investigated.
{"title":"A New Flexible Probability Model: Theory, Estimation and Modeling Bimodal Left Skewed Data","authors":"Mohamed Aboraya, M. M. Ali, Haitham M. Yousof, Mohamed ibrahim Mohamed","doi":"10.18187/pjsor.v18i2.3938","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.3938","url":null,"abstract":"In this work, we introduced a new three-parameter Nadarajah-Haghighi model. We derived explicit expressions for some of it statistical properties. The Farlie Gumbel Morgenstern, modified Farlie Gumbel Morgenstern, Clayton, Renyi and Ali-Mikhail-Haq copulas are used for deriving some bivariate type extensions. We consider maximum likelihood, Cramér-von-Mises, ordinary least squares, whighted least squares, Anderson Darling, right tail Anderson Darling and left tail Anderson Darling estimation procedures to estimate the unknown model parameters. Simulation study for comparing estimation methods is performed. An application for comparing methods as also presented. The maximum likelihood estimation method is the best method. However, the other methods performed well. Another application for comparing the competitive models is investigated.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48500841","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 : 2022-06-02DOI: 10.18187/pjsor.v18i2.3976
E. Barili, J. Achcar, R. P. Oliveira
Climate change has been observed worldwide in the last years. Among the different effects of climate change, rain precipitation is one of the effects that most challenge the population of all countries in the world. The main goal of this study is to introduce a data analysis of monthly rainfall data related to five countries in Central Asia (Kazakhstan, Kyrgyzstan, Tadjikistan, Turkmenistan and Uzbekistan) for a long period of time to discover the behavior of rain precipitation in these countries in the last decades and possible link with climate change. Since climate data are positive real values, Weibull regression models are used in the data analysis in presence of some spatial factors as latitude and longitude of the climate stations in each country, temporal factors (linear year effects), altitude of the climate station and categorical factors (countries).The obtained results show that some factors have different effects in the monthly rainfall of the assumed countries during the follow-up assumed period, possibly linked to the climate change observed in the last decades worldwide.
{"title":"Spatial-temporal factors affecting monthly rainfall in some Central Asian countries assuming a Weibull regression model","authors":"E. Barili, J. Achcar, R. P. Oliveira","doi":"10.18187/pjsor.v18i2.3976","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.3976","url":null,"abstract":"Climate change has been observed worldwide in the last years. Among the different effects of climate change, rain precipitation is one of the effects that most challenge the population of all countries in the world. The main goal of this study is to introduce a data analysis of monthly rainfall data related to five countries in Central Asia (Kazakhstan, Kyrgyzstan, Tadjikistan, Turkmenistan and Uzbekistan) for a long period of time to discover the behavior of rain precipitation in these countries in the last decades and possible link with climate change. Since climate data are positive real values, Weibull regression models are used in the data analysis in presence of some spatial factors as latitude and longitude of the climate stations in each country, temporal factors (linear year effects), altitude of the climate station and categorical factors (countries).The obtained results show that some factors have different effects in the monthly rainfall of the assumed countries during the follow-up assumed period, possibly linked to the climate change observed in the last decades worldwide.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46368387","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 : 2022-06-01DOI: 10.18187/pjsor.v18i2.2996
Faiz Bin Zulkifli, Zulkifley Bin Mohmed, N. Azmee
The Huber M-estimator is proposed in this study as a robust method for estimating the parameters of the cumulative odds model, which includes a logistic link function and polytomous explanatory variables. With the help of an intensive Monte Carlo simulation study carried out using the statistical software R, this study evaluates the performance of the maximum likelihood estimator (MLE) and the robust technique developed. Bias, RMSE, and the Lipsitz Statistic are used to measure comparisons. When conducting the simulation study, different sample sizes, contamination proportions, and error standard deviations are considered. Preliminary findings indicate that the M-estimator with Huber weight estimates produces the best results for parameter estimation and overall model fitting compared to the MLE. As an illustration, the procedure is applied to real-world data of students' final exam grades as measured by two different estimators.
本研究提出Huber m -估计量作为累积机率模型参数估计的鲁棒方法，该模型包含一个逻辑连结函数和多个解释变量。在使用统计软件R进行的密集蒙特卡罗模拟研究的帮助下，本研究评估了最大似然估计器(MLE)的性能和开发的鲁棒技术。偏倚、均方根误差和利普西统计量被用来衡量比较。在进行模拟研究时，考虑了不同的样本量、污染比例和误差标准偏差。初步结果表明，与MLE相比，带有Huber权值估计的m估计器在参数估计和整体模型拟合方面产生了最好的结果。作为一个例子，该过程应用于学生期末考试成绩的真实数据，由两个不同的估计器测量。
{"title":"Huber M-estimator for Cumulative Odds Model with Application to the Measurement of Students' Final Exam Grades","authors":"Faiz Bin Zulkifli, Zulkifley Bin Mohmed, N. Azmee","doi":"10.18187/pjsor.v18i2.2996","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.2996","url":null,"abstract":"The Huber M-estimator is proposed in this study as a robust method for estimating the parameters of the cumulative odds model, which includes a logistic link function and polytomous explanatory variables. With the help of an intensive Monte Carlo simulation study carried out using the statistical software R, this study evaluates the performance of the maximum likelihood estimator (MLE) and the robust technique developed. Bias, RMSE, and the Lipsitz Statistic are used to measure comparisons. When conducting the simulation study, different sample sizes, contamination proportions, and error standard deviations are considered. Preliminary findings indicate that the M-estimator with Huber weight estimates produces the best results for parameter estimation and overall model fitting compared to the MLE. As an illustration, the procedure is applied to real-world data of students' final exam grades as measured by two different estimators.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45719525","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 : 2022-06-01DOI: 10.18187/pjsor.v18i2.3515
E. Elsherpieny, E. Almetwally
In this paper, we introduce the exponentiated generalized alpha power family of distributions to extend the several other distributions. We used the new family to discuss the exponentiated generalized alpha power exponential (EGAPEx) distribution. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by the maximum likelihood estimation (MLE), maximum product spacing (MPS) and Bayesian estimation methods. A Monte Carlo Simulation is performed to compare between different methods. We illustrate the performance of the proposed new family of distributions by means of two real data sets and the data sets show the new family of distributions is more appropriate as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions.
{"title":"The Exponentiated Generalized Alpha Power Family of Distribution: Properties and Applications","authors":"E. Elsherpieny, E. Almetwally","doi":"10.18187/pjsor.v18i2.3515","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.3515","url":null,"abstract":"In this paper, we introduce the exponentiated generalized alpha power family of distributions to extend the several other distributions. We used the new family to discuss the exponentiated generalized alpha power exponential (EGAPEx) distribution. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by the maximum likelihood estimation (MLE), maximum product spacing (MPS) and Bayesian estimation methods. A Monte Carlo Simulation is performed to compare between different methods. We illustrate the performance of the proposed new family of distributions by means of two real data sets and the data sets show the new family of distributions is more appropriate as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48898445","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 : 2022-06-01DOI: 10.18187/pjsor.v18i2.3921
Rather Khalid, E. Koçyiğit, Ceren Ünal
In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the exponential function for the population mean in case of non-response for simple random sampling for the estimation of the mean of the population with the RSS (ranked set sampling) method. The equations for the MSE and the bias of the adapted estimators are obtained for RSS and it in theory shows that the proposed estimator is additional efficient than the present RSS mean estimators in the literature. In addition, we support these theoretical results with real COVID-19 real data and conjointly the simulation studies with different distributions and parameters. As a result of the study, it was observed that the efficiency of the proposed estimator was better than the other estimators.
{"title":"New Exponential Ratio Estimator in Ranked Set Sampling","authors":"Rather Khalid, E. Koçyiğit, Ceren Ünal","doi":"10.18187/pjsor.v18i2.3921","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.3921","url":null,"abstract":"In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the exponential function for the population mean in case of non-response for simple random sampling for the estimation of the mean of the population with the RSS (ranked set sampling) method. The equations for the MSE and the bias of the adapted estimators are obtained for RSS and it in theory shows that the proposed estimator is additional efficient than the present RSS mean estimators in the literature. In addition, we support these theoretical results with real COVID-19 real data and conjointly the simulation studies with different distributions and parameters. As a result of the study, it was observed that the efficiency of the proposed estimator was better than the other estimators.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46438396","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 : 2022-06-01DOI: 10.18187/pjsor.v18i2.3319
A. Gaire, G. B. Thapa, S. K. C.
In this paper, polynomial models have been formulated to describe the distribution pattern of age-specific fertility rates (ASFRs) and forward-cumulative ASFRs of Nepali mothers. The former follows the bi-quadratic polynomial and the latter follows the quadratic one. Velocity and elasticity equations of the fitted models have been formulated. The areas covered by the curves of the fitted models have been evaluated, and the area covered by the curve of ASFRs is equivalent to the total fertility rate (TFR). Furthermore, the mode of the fitted ASFRs has been estimated. To test the stability and validity of fitted models, cross validity prediction power, shrinkage of the model, F-test statistics and the coefficient of determination have been applied.
{"title":"Mathematical Modeling of Age-Specific Fertility Rates of Nepali Mothers","authors":"A. Gaire, G. B. Thapa, S. K. C.","doi":"10.18187/pjsor.v18i2.3319","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.3319","url":null,"abstract":"In this paper, polynomial models have been formulated to describe the distribution pattern of age-specific fertility rates (ASFRs) and forward-cumulative ASFRs of Nepali mothers. The former follows the bi-quadratic polynomial and the latter follows the quadratic one. Velocity and elasticity equations of the fitted models have been formulated. The areas covered by the curves of the fitted models have been evaluated, and the area covered by the curve of ASFRs is equivalent to the total fertility rate (TFR). Furthermore, the mode of the fitted ASFRs has been estimated. To test the stability and validity of fitted models, cross validity prediction power, shrinkage of the model, F-test statistics and the coefficient of determination have been applied.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45775865","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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