Authors:Fatemeh Moslemi, Habibeh Sadeghi Pages: 1 - 12 Abstract: The relationship between the reference-uncooperative linear bilevel two-follower decision making and the multi-objective decision making has been recently considered (Sadeghi and Moslemi, 2019). In this paper, we address the foregoing relation for the uncooperative linear bilevel multi-follower programming (ULBMFP) model with followers. Furthermore, we consider some geometric properties of the feasible solutions set of the ULBMFP problem. Moreover an algorithm to find an optimal solution for the ULBMFP problem was proposed. Ultimately, some numerical examples to illustrate the proposed algorithm were provided. PubDate: 2022-03-01 DOI: 10.18187/pjsor.v18i1.3261

Authors:Kubra Bagci, Necati Erdogan, Talha Arslan, H. Eray Celik Pages: 13 - 25 Abstract: In this study, an alpha power inverted Kumaraswamy (APIK) distribution is introduced. The APIK distribution is de- rived by applying alpha power transformation to an inverted Kumaraswamy distribution. Some submodels and limiting cases of the APIK distribution are obtained as well. To the best of the authors’ knowledge, some of these distributions have not been introduced yet. Statistical inference of the APIK distribution, including survival and hazard rate func- tions, are obtained. Unknown parameters of the APIK distribution are estimated by using the maximum likelihood (ML), maximum product of spacings (MPS), and least squares (LS) methods. A Monte Carlo simulation study is con- ducted to compare the efficiencies of the ML estimators of the shape parameters α, β and λ of the APIK distribution with their MPS and LS counterparts. An application to a real data set is provided to show the implementation and modeling capability of the APIK distribution. PubDate: 2022-03-01 DOI: 10.18187/pjsor.v18i1.3327

Authors:G.G. Hamedani, Mahrokh Najaf Pages: 27 - 32 Abstract: Chesneau and Palacios considered the inﬁnite decomposability of the Geometric (Chesneau and Palacios(2021b), (paper 1)), and Gamma, Laplace and n-Laplace (Chesneau and Palacios(2021a), (paper 2)) of two (as well as n) independent random variables. They obtained, very nicely, certain important results on the decomposability concept. Also, George Yanev published a paper entitled” Exponential and Hyper exponential Distributions: Some Characterizations” (Yanev G.(2020), (paper 3)) and reported a paper entitled ”On Arnold-Villasenor Conjectures for Characterizing Exponential Distribution Based on Sample of Size Three” (Yanev(2020), (paper 4)). In both papers, George Yanev considered the distribution of the sum or a linear combination of the independent random variables. Yanev obtained certain nice results in these two papers under the assumption of independence of the summands. Roozegar and Bazyani published a paper entitled ”Exact Distribution of Random Weighted Convolution of Some Beta Distributions Through an Integral Transform” (Roozegar and Bazyari(2017), (paper 5)), in which they considered the exact distribution of the weighted average of n independent beta random variables and provided a new integral transformation with some of its mathematical properties. Ahmad et al.(2021) considered ”Compound Negative Binomial Distribution as the Sum of Independent Laplace Variates” (paper 6) and discussed inﬁnite divisibility of the underlining distribution. Furthermore, Marques et al.(2015) considered the distribution of the linear combinations of independent Gumbel random variables and obtain, very nicely, certain important results (paper 7). In this short note, we like to show that the very strong assumption of ”independence” can be replaced with a much weaker assumption of ”sub-independence” in all aforementioned papers. This short paper may be helpful to other investigators dealing with the random variables which are not necessary independent, but could be sub-independent. PubDate: 2022-03-02 DOI: 10.18187/pjsor.v18i1.3553

Authors:Broderick Oluyede, Peter O. Peter, Nkumbuludzi Ndwapi, Huybrechts Bindele Pages: 33 - 57 Abstract: A new family of distributions called exponentiated half-logistic Odd Burr III-G (EHL-OBIII-G) is developed and studied. Mathematical and statistical properties such as the hazard function, quantile function, moments, probability weighted moments, Renyi entropy and stochastic orders are derived. The model parameters are estimated based on the maximum likelihood estimation method. The usefulness of the proposed family of distributions is demonstrated via extensive simulation studies. Finally the proposed model and its special case is applied to real data sets to illustrate its best fit and flexibility. PubDate: 2022-03-02 DOI: 10.18187/pjsor.v18i1.3668

Authors:Faihatuz Zuhairoh, Dedi Rosadi Pages: 59 - 69 Abstract: COVID-19 has spread throughout the world, including in Southeast Asia. Many studies have made predictions using various models. However, very few are data-driven based. Meanwhile for the COVID-19 case, which is still ongoing, it is very suitable to use data-driven approach with phenomenological models. This paper aimed to obtain effective forecasting models and then predict when COVID-19 in Southeast Asia will peak and end using daily cumulative case data. The research applied the Richards curve and the logistic growth model, combining the two models to make prediction of the COVID-19 cases in Southeast Asia, both the countries with one pandemic wave or those with more than one pandemic wave. The best prediction results were obtained using the Richards curve with the logistic growth model parameters used as the initial values. In the best scenario, the Southeast Asia region is expected to be free from the COVID-19 pandemic at the end of 2021. These modeling results are expected to provide information about the provision of health facilities and how to handle infectious disease outbreaks in the future. PubDate: 2022-03-02 DOI: 10.18187/pjsor.v18i1.3714

Authors:VILAYAT ALI BHAT, Sudesh Pundir Pages: 71 - 84 Abstract: This manuscript aims to study the intervention-based probability model. Statistical and reliability properties such as the expressions for, cumulative density function (CDF), mean deviations about mean and median, rth order central and non-central moments, ”generation functions” for moments have been derived. Moreover, the expression for reliability function, hazard rate, reverse hazard rate, aging intensity, mean residual life function, stress-strength reliability, and entropy metrics due to R´enyi and Shannon are also derived. Monte Carlo simulation study performance of maximum likelihood estimates (MLEs) has been carried out, followed by calculations of Average Bias (ABias), and Mean Square Error (MSE). The applicability of the model in real-life situations has been discussed by analyzing the two real-life data sets. PubDate: 2022-03-02 DOI: 10.18187/pjsor.v18i1.3829

Authors:Naveen K. Bansal, V.S. Vaidyanathan, P. Chandrasekhar Pages: 85 - 97 Abstract: In this paper, by considering an M M 1 ∞ queueing model, Bayes estimators of traﬃc intensity and measures of system performance are worked out under squared error loss function (SELF) based on observed data on the independent interarrival and service times. Further, minimum posterior risk associated with Bayes estimators of traﬃc intensity and system performance measures are obtained under SELF. Numerical illustration of the performance of the estimates is given through simulation study. It is shown that Bayes estimators perform better than the maximum likelihood estimators under the influence of prior information. PubDate: 2022-03-02 DOI: 10.18187/pjsor.v18i1.3904

Authors:Zubair Ahmad, Eisa Mahmoudi, Rasool Roozegarz, G.G. Hamedani, Nadeem Shafique Butt Pages: 99 - 120 Abstract: In the past couple of years, statistical models have been extensively used in applied areas for analyzing real data sets. However, in numerous situations, the traditional distributions are not ﬂexible enough to cater to different aspects of the real phenomena. For example, (i) in the practice of reliability engineering and biomedical analysis, some distributions provide the best ﬁt to the data having monotonic failure rate function, but fails to provide the best ﬁt to the data having non-monotonic failure rate function, (ii) some statistical distributions provide the best ﬁt for small insurance losses, but fails to provide an adequate ﬁt to large claim size data, and (iii) some distributions do not have closed forms causing difﬁculties in the estimation process. To address the above issues, therefore, several methods have been suggested to improve the ﬂexibility of the classical distributions. In this article, we investigate some of the former methods of generalizing the existing distributions. Further, we propose nineteen new methods of extending the classical distributions to obtain ﬂexible models suitable for modeling data in applied ﬁelds. We also provide certain characterizations of the newly proposed families. Finally, we provide a comparative study of the newly proposed and some other existing well-known models via analyzing three real data sets from three different disciplines such as reliability engineering, medical, and ﬁnancial sciences. PubDate: 2022-03-02 DOI: 10.18187/pjsor.v18i1.3908

Authors:Md. Shohel Rana, Saman Hanif Shahbaz, Muhammad Qaiser Shahbaz, Md. Mahabubur Rahman Pages: 121 - 132 Abstract: In the present study, we propose a new family of distributions namely the Pareto-X family. A sub model of the proposed family called Pareto-Weibull (PW) distribution is discussed. The maximum likelihood estimators of the model parameters are obtained. Different distributional properties of the distribution are described. In order to assess the applicability of the model, two real-life applications from environmental and biological study are considered. The practical applications show that the proposed model provides better fitness than any other models used in this study. PubDate: 2022-03-02 DOI: 10.18187/pjsor.v18i1.3821

Authors:Wahid Shehata, Murtadha Mansour Abdullah, Mohamed K. A. Refaie Pages: 133 - 149 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. PubDate: 2022-03-04 DOI: 10.18187/pjsor.v18i1.3268

Authors:Sema Akin Bas, Hale Gonce Kocken, Beyza Ahlatcioglu Ozkok Pages: 151 - 166 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. PubDate: 2022-03-04 DOI: 10.18187/pjsor.v18i1.3889

Authors:Sirinapa Aryuyuen Pages: 167 - 177 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. PubDate: 2022-03-04 DOI: 10.18187/pjsor.v18i1.2988

Authors:Amal Soliman Hassan, Rokaya Elmorsy Mohamed, Omid Kharazmi, Heba Fathy Nagy Pages: 179 - 193 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. PubDate: 2022-03-04 DOI: 10.18187/pjsor.v18i1.3872

Authors:Suleman Nasiru, Abdul Ganiyyu Abubakari Pages: 195 - 210 Abstract: A new class of distributions called Marshall-Olkin Zubair-G family is proposed in this study. Some statistical properties of the family are derived and two special distributions namely, Marshall-Olkin Zubair Nadarajah-Haghighi and Marshall-Olkin Zubair Weibull distributions are developed. The plots of the density and hazard rate functions of the special distributions exhibit different shapes for chosen parameter values, making them good candidates for modeling different types of datasets. A real life application using the Marshall-Olkin Zubair Nadarajah-Haghighi distribution revealed that it performs better than other existing extensions of the Nadarajah-Haghighi distribution for the given dataset. PubDate: 2022-03-04 DOI: 10.18187/pjsor.v18i1.3096

Authors:Mahfooz Alam, Rafiqullah Khan, Mohd. Azam khan Pages: 211 - 224 Abstract: In this paper, we use the concept of dual generalized order statistics dgos which was given by Pawlas and Syznal (2001). By using this, we obtain the various theorems and some relations through ratio and inverse moment by using exponentiated-Weibull distribution. Cases for order statistics and lower record values are also considered. Further, we characterize the exponentiated-Weibull distribution through three different methods by using the results obtained in this paper. PubDate: 2022-03-04 DOI: 10.18187/pjsor.v18i1.3810

Authors:Lazhar Benkhelifa Pages: 225 - 243 Abstract: In this paper, we propose a new flexible lifetime distribution. The proposed distribution will be referred to as beta power Muth distribution. It can be used to model increasing, decreasing, bathtub shaped or upside-down bathtub hazard rates. Some properties of the new model are obtained including moments, quantile function and moments of the order statistics. The unknown model parameters are estimated by the maximum likelihood method of estimation. A Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates. Two reliability data sets are applied to illustrate the usefulness and flexibility of the proposed model. In addition, we introduce a new location-scale regression model based on the logarithm of the proposed distribution and provide a real data application. PubDate: 2022-03-04 DOI: 10.18187/pjsor.v18i1.3529

Authors:Ibrahim A. Ahmad, Netti Herawati Pages: 245 - 248 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. PubDate: 2022-03-05 DOI: 10.18187/pjsor.v18i1.3746

Authors:Wahid A. M. Shehata, Nadeem Shafique Butt, Haitham Yousof, Mohamed Aboraya Pages: 249 - 272 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. PubDate: 2022-03-05 DOI: 10.18187/pjsor.v18i1.3930

Authors:Housila Prasad Singh, Pragati Nigam Pages: 273 - 296 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. PubDate: 2022-03-06 DOI: 10.18187/pjsor.v18i1.3507

Authors:Mai Hegazy, Rabab Abd EL-Kader, Gannat AL-Dayian, Abeer Abd-Alla EL-Helbawy Pages: 297 - 328 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. PubDate: 2022-03-06 DOI: 10.18187/pjsor.v18i1.3634