Pub Date : 2022-06-01DOI: 10.18187/pjsor.v18i2.3533
Mujiati Dwi Kartikasari, N. Hikmah
Forecasting is one of the activities needed by companies to determine the policies that need to be taken for the continuity of operations. There are many methods for forecasting, one of which is the grey model GM(1,1). The GM(1,1) is one of the successful forecasting methods applied to economics, finance, engineering, and others. However, according to several previous study, the GM(1,1) is not good enough to forecast data containing seasonal characteristics. Therefore, the aim of this study is to develop hybrid model so that the GM(1,1) is able to forecast seasonal time series. The hybrid model is constructed by combining decomposition method for seasonality adjustment and grey model GM(1,1) for forecasting seasonal time series. The results are compared to seasonal grey model SGM(1,1). Based on the evaluation using error criteria, it is found that the hybrid model is the best model.
{"title":"Decomposition Method with Application of Grey Model GM(1,1) for Forecasting Seasonal Time Series","authors":"Mujiati Dwi Kartikasari, N. Hikmah","doi":"10.18187/pjsor.v18i2.3533","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.3533","url":null,"abstract":"Forecasting is one of the activities needed by companies to determine the policies that need to be taken for the continuity of operations. There are many methods for forecasting, one of which is the grey model GM(1,1). The GM(1,1) is one of the successful forecasting methods applied to economics, finance, engineering, and others. However, according to several previous study, the GM(1,1) is not good enough to forecast data containing seasonal characteristics. Therefore, the aim of this study is to develop hybrid model so that the GM(1,1) is able to forecast seasonal time series. The hybrid model is constructed by combining decomposition method for seasonality adjustment and grey model GM(1,1) for forecasting seasonal time series. The results are compared to seasonal grey model SGM(1,1). Based on the evaluation using error criteria, it is found that the hybrid model is the best model.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44284598","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.v18i2.2767
D. Devianto, Stefi Amalia Fitri, Hazmira Yoza, M. Maiyastri
The infinite divisibility of compound negative binomial distribution especially as the sum of Laplace distribution has important roles in governing the mathematical model based on its characteristic function. In order to show the property of characteristic function of this compound negative binomial distribution, it is used Fourier-Stieltjes transform to have characteristic function and then governed the property of continuity and quadratic form by using analytical approaches. The infinite divisibility property is obtained by introducing a function satisfied the criteria to be a characteristic function such that its convolution has the characteristic function of compound negative binomial distribution. Then it is concluded that the characteristic function of compound negative binomial distribution as the sum of Laplace distribution satisfies the property of continuity, quadratic form and infinite divisibility.
{"title":"The Infinite Divisibility of Compound Negative Binomial Distribution as the Sum of Laplace Distribution","authors":"D. Devianto, Stefi Amalia Fitri, Hazmira Yoza, M. Maiyastri","doi":"10.18187/pjsor.v18i2.2767","DOIUrl":"https://doi.org/10.18187/pjsor.v18i2.2767","url":null,"abstract":"The infinite divisibility of compound negative binomial distribution especially as the sum of Laplace distribution has important roles in governing the mathematical model based on its characteristic function. In order to show the property of characteristic function of this compound negative binomial distribution, it is used Fourier-Stieltjes transform to have characteristic function and then governed the property of continuity and quadratic form by using analytical approaches. The infinite divisibility property is obtained by introducing a function satisfied the criteria to be a characteristic function such that its convolution has the characteristic function of compound negative binomial distribution. Then it is concluded that the characteristic function of compound negative binomial distribution as the sum of Laplace distribution satisfies the property of continuity, quadratic form and infinite divisibility.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44435504","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 : 2022-03-06DOI: 10.18187/pjsor.v18i1.3507
Housila Prasad Singh, P. Nigam
In this paper we consider a two parameter ratio-product-ratio estimator for estimating population mean in case of post stratification following the estimator due to Chami et al (2012). The bias and mean squared error of proposed estimator are obtained to the first degree of approximation. We derive conditions under which the proposed estimator has smaller mean squared error than the sample mean , ratio estimator and product estimators . Empirical studies gives insight on the magnitude of the efficiency of the estimator developed.
{"title":"A Two Parameter Ratio-Product-Ratio Estimator in Post Stratification","authors":"Housila Prasad Singh, P. Nigam","doi":"10.18187/pjsor.v18i1.3507","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.3507","url":null,"abstract":"In this paper we consider a two parameter ratio-product-ratio estimator for estimating population mean in case of post stratification following the estimator due to Chami et al (2012). The bias and mean squared error of proposed estimator are obtained to the first degree of approximation. We derive conditions under which the proposed estimator has smaller mean squared error than the sample mean , ratio estimator and product estimators . Empirical studies gives insight on the magnitude of the efficiency of the estimator developed.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43248658","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 : 2022-03-06DOI: 10.18187/pjsor.v18i1.3634
M. Hegazy, Rabab Abd EL-Kader, G. Al-Dayian, A. EL-Helbawy
In this paper, a discrete inverted Kumaraswamy distribution; which is a discrete version of the continuous inverted Kumaraswamy variable, is derived using the general approach of discretization of a continuous distribution. Some important distributional and reliability properties of the discrete inverted Kumaraswamy distribution are obtained. Maximum likelihood and Bayesian approaches are applied to estimate the model parameters. A simulation study is carried out to illustrate the theoretical results. Finally, a real data set is applied.
{"title":"Discrete Inverted Kumaraswamy Distribution: Properties and Estimation","authors":"M. Hegazy, Rabab Abd EL-Kader, G. Al-Dayian, A. EL-Helbawy","doi":"10.18187/pjsor.v18i1.3634","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.3634","url":null,"abstract":"In this paper, a discrete inverted Kumaraswamy distribution; which is a discrete version of the continuous inverted Kumaraswamy variable, is derived using the general approach of discretization of a continuous distribution. Some important distributional and reliability properties of the discrete inverted Kumaraswamy distribution are obtained. Maximum likelihood and Bayesian approaches are applied to estimate the model parameters. A simulation study is carried out to illustrate the theoretical results. Finally, a real data set is applied.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49138974","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 : 2022-03-05DOI: 10.18187/pjsor.v18i1.3746
I. Ahmad, N. Herawati
For a sequence of independent non-identically distributed random variables with positive means, rates of convergence of the maximum of their sums are established. These rates are exact and are obtained under the same moment conditions as those used for partial sums.
{"title":"Convergence Rates of Maxima of Non-identical Sums","authors":"I. Ahmad, N. Herawati","doi":"10.18187/pjsor.v18i1.3746","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.3746","url":null,"abstract":"For a sequence of independent non-identically distributed random variables with positive means, rates of convergence of the maximum of their sums are established. These rates are exact and are obtained under the same moment conditions as those used for partial sums.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42175293","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 : 2022-03-05DOI: 10.18187/pjsor.v18i1.3930
Wahid A. M. Shehata, Nadeem Shafique Butt, H. Yousof, Mohamed Aboraya
In this article, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index are performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "monotonically decreasing", " monotonically increasing", "increasing-constant”, “upside-down-constant", "decreasing-constant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The applicability of the new life distribution is illustrated by means of two real data sets.
{"title":"A New Lifetime Parametric Model for the Survival and Relief Times with Copulas and Properties","authors":"Wahid A. M. Shehata, Nadeem Shafique Butt, H. Yousof, Mohamed Aboraya","doi":"10.18187/pjsor.v18i1.3930","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.3930","url":null,"abstract":"In this article, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index are performed. The new density can be right skewed and symmetric with \"unimodal\" and \"bimodal\" shapes. The new hazard function can be \"constant\", \"monotonically decreasing\", \" monotonically increasing\", \"increasing-constant”, “upside-down-constant\", \"decreasing-constant\". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The applicability of the new life distribution is illustrated by means of two real data sets.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47097047","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 : 2022-03-04DOI: 10.18187/pjsor.v18i1.3268
Wahid A. M. Shehata, M. Abdullah, Mohamed K. A. Refaie
In this paper, we introduce a new continuous log-logistic extension. Several of its properties are established. A numerical analysis for skewness and kurtosis is presented. The new failure rate can be "bathtub or U shaped", "increasing", "decreasing-constant", "J shaped", "constant" and "decreasing". Many bivariate and Multivariate type distributions are derived using the Clayton Copula and the Morgenstern family. To assess of the finite sample behavior of the estimators, we performed a graphical simulation. Some useful applications are considered for supporting the new model.
{"title":"A novel four-parameter log-logistic model: mathematical properties and applications to breaking stress, survival times and leukemia data","authors":"Wahid A. M. Shehata, M. Abdullah, Mohamed K. A. Refaie","doi":"10.18187/pjsor.v18i1.3268","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.3268","url":null,"abstract":"In this paper, we introduce a new continuous log-logistic extension. Several of its properties are established. A numerical analysis for skewness and kurtosis is presented. The new failure rate can be \"bathtub or U shaped\", \"increasing\", \"decreasing-constant\", \"J shaped\", \"constant\" and \"decreasing\". Many bivariate and Multivariate type distributions are derived using the Clayton Copula and the Morgenstern family. To assess of the finite sample behavior of the estimators, we performed a graphical simulation. Some useful applications are considered for supporting the new model.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48427165","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 : 2022-03-04DOI: 10.18187/pjsor.v18i1.3889
Sema Akin Bas, Hale Gonce Kocken, Beyza Ahlatcioglu Ozkok
The linear fractional transportation problem (LFTP) is widely encountered as a particular type of transportation problem (TP) in real-life. In this paper, a novel algorithm, based on the traditional definition of continuity, is presented to solve the LFTP. An iterative constraint is constructed by combining the objective function of the LFTP and the supply-demand condition since the fractional objective function is continuous at every point of the feasible region. By this constraint obtained, LFTP is converted into an iterative linear programming (LP) problem to reach the optimum solution. In this study, the case of asymptotic solution for LFTP is discussed for the first time in the literature. The numerical examples are performed for the linear and asymptotic cases to illustrate the method, and the approach proposed is compared with the other existing methods to demonstrate the efficiency of the algorithm. Also, an application had environmentalist objective is solved by proposed mathematical method using the software general algebraic modeling system (GAMS) with data set of the real case. Finally, some computational results from tests performed on randomly generated large-scale transportation problems are provided.
{"title":"A novel iterative method to solve a linear fractional transportation problem","authors":"Sema Akin Bas, Hale Gonce Kocken, Beyza Ahlatcioglu Ozkok","doi":"10.18187/pjsor.v18i1.3889","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.3889","url":null,"abstract":"The linear fractional transportation problem (LFTP) is widely encountered as a particular type of transportation problem (TP) in real-life. In this paper, a novel algorithm, based on the traditional definition of continuity, is presented to solve the LFTP. An iterative constraint is constructed by combining the objective function of the LFTP and the supply-demand condition since the fractional objective function is continuous at every point of the feasible region. By this constraint obtained, LFTP is converted into an iterative linear programming (LP) problem to reach the optimum solution. In this study, the case of asymptotic solution for LFTP is discussed for the first time in the literature. The numerical examples are performed for the linear and asymptotic cases to illustrate the method, and the approach proposed is compared with the other existing methods to demonstrate the efficiency of the algorithm. Also, an application had environmentalist objective is solved by proposed mathematical method using the software general algebraic modeling system (GAMS) with data set of the real case. Finally, some computational results from tests performed on randomly generated large-scale transportation problems are provided.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45067359","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 : 2022-03-04DOI: 10.18187/pjsor.v18i1.3872
A. Hassan, R. Mohamed, O. Kharazmi, H. Nagy
In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through the Kumaraswamy family. The proposed model is referred to as the Kumaraswamy extended exponential (KwEE). The significance of the suggested distribution from its flexibility in applications and data modeling. As specific sub-models, it includes the exponential, Kumaraswamy exponential, Kumaraswamy Lindley, Lindley, extended exponential, exponentiated Lindley, gamma and generalized exponential distributions. The representation of the density function, quantile function, ordinary and incomplete moments, generating function, and reliability of the KwEE distribution are all derived. The maximum likelihood approach is used to estimate model parameters. A simulation study for maximum likelihood estimates was used to investigate the behaviour of the model parameters. A numerical analysis is performed for various sample sizes and parameter values to analyze the behaviour of estimates using accuracy measures. According to a simulated investigation, the KwEE's maximum likelihood estimates perform well with increased sample size. We provide two real-world examples utilizing applied research to demonstrate that the new model is more effective.
{"title":"A New Four Parameter Extended Exponential Distribution with Statistical Properties and Applications","authors":"A. Hassan, R. Mohamed, O. Kharazmi, H. Nagy","doi":"10.18187/pjsor.v18i1.3872","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.3872","url":null,"abstract":"In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through the Kumaraswamy family. The proposed model is referred to as the Kumaraswamy extended exponential (KwEE). The significance of the suggested distribution from its flexibility in applications and data modeling. As specific sub-models, it includes the exponential, Kumaraswamy exponential, Kumaraswamy Lindley, Lindley, extended exponential, exponentiated Lindley, gamma and generalized exponential distributions. The representation of the density function, quantile function, ordinary and incomplete moments, generating function, and reliability of the KwEE distribution are all derived. The maximum likelihood approach is used to estimate model parameters. A simulation study for maximum likelihood estimates was used to investigate the behaviour of the model parameters. A numerical analysis is performed for various sample sizes and parameter values to analyze the behaviour of estimates using accuracy measures. According to a simulated investigation, the KwEE's maximum likelihood estimates perform well with increased sample size. We provide two real-world examples utilizing applied research to demonstrate that the new model is more effective.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44600166","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 : 2022-03-04DOI: 10.18187/pjsor.v18i1.2988
S. Aryuyuen
In this paper, a new mixture distribution for count data, namely the negative binomial-new generalized Lindley (NB-NGL) distribution is proposed. The NB-NGL distribution has four parameters, and is a flexible alternative for analyzing count data, especially when there is over-dispersion in the data. The proposed distribution has sub-models such as the negative binomial-Lindley (NB-L), negative binomial-gamma (NB-G), and negative binomial-exponential (NB-E) distributions as the special cases. Some properties of the proposed distribution are derived, i.e., the moments and order statistics density function. The unknown parameters of the NB-NGL distribution are estimated by using the maximum likelihood estimation. The results of the simulation study show that the maximum likelihood estimators give the parameter estimates close to the parameter when the sample is large. Application of NB-NGL distribution is carry out on three samples of medical data, industry data, and insurance data. Based on the results, it is shown that the proposed distribution provides a better fit compared to the Poisson, negative binomial, and its sub-model for count data.
{"title":"The Negative Binomial-New Generalized Lindley Distribution for Count Data: Properties and Application","authors":"S. Aryuyuen","doi":"10.18187/pjsor.v18i1.2988","DOIUrl":"https://doi.org/10.18187/pjsor.v18i1.2988","url":null,"abstract":"In this paper, a new mixture distribution for count data, namely the negative binomial-new generalized Lindley (NB-NGL) distribution is proposed. The NB-NGL distribution has four parameters, and is a flexible alternative for analyzing count data, especially when there is over-dispersion in the data. The proposed distribution has sub-models such as the negative binomial-Lindley (NB-L), negative binomial-gamma (NB-G), and negative binomial-exponential (NB-E) distributions as the special cases. Some properties of the proposed distribution are derived, i.e., the moments and order statistics density function. The unknown parameters of the NB-NGL distribution are estimated by using the maximum likelihood estimation. The results of the simulation study show that the maximum likelihood estimators give the parameter estimates close to the parameter when the sample is large. Application of NB-NGL distribution is carry out on three samples of medical data, industry data, and insurance data. Based on the results, it is shown that the proposed distribution provides a better fit compared to the Poisson, negative binomial, and its sub-model for count data.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42709498","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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