Pakistan Journal of Statistics and Operation Research
Not a member yet
861 research outputs found
Sort by
A New Family of Heavy-Tailed Generalized Topp-Leone-G Distributions with Application
No full textIn this article, we introduce a robust generalization of the generalized Topp-Leone-G (GEN-TL-G) family of distributions via the heavy-tailed technique. The distribution is named heavy-tailed generalized Topp-Leone-G (HT-GEN-TL-G) family of distributions. Statistical properties of the HT-GEN-TL-G family of distributions including reliability functions, quantile function, density expansion, moments, moment generating function, incomplete moments, Rényi entropy, distribution of order statistics are derived. Different estimation methods including Maximum Likelihood, Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cram\'er-von Mises and Maximum Product of Spacing are utilized to estimate the unknown parameters of the new distribution, and a simulation study is used to compare the results of the estimation methods. Risk measures for this distribution were also developed and finally the effectiveness of this new family of distributions was demonstrated using applications to two real data sets
Evaluating the Efficiency of Turkish Banking Sector Using Data Envelopment Analysis and Malmquist Productivity Index: Covid-19 Pandemic and After
No full textCovid-19 pandemic has created a deep crisis with social, cultural, economic, and political consequences all over the world. In this study, we used the Malmquist Total Factor Productivity Change Index (TFPCH) and Data Envelopment Analysis (DEA) methods to assess the efficiency and performance of banks during the Covid-19 pandemic and in the post-pandemic era. We performed the application for 17 banks in Türkiye of which data structure is suitable for analysis. For the analysis, data from 2019, the beginning of the Covid-19 epidemic, to 2022, when the epidemic almost ended, were used. The highest value of the general efficiency average of banks is 0.943 in 2020. 2020 is also the year with the highest number of effective banks with a total of 9 effective banks. The highest value of the TFPCH general average is 1.543 in the 2021-2022 period. It was determined that the state banks had the highest average efficiency percentage and the highest TFPCH average for the entire period of 2019-2022
Designing a variable control chart for a two-stage production process
No full textIn this paper, a variable chart has been proposed to study a two-stage serial production process. Measurements of quality characteristics of products processed at each stage are assumed to be independent and follow normal distribution. In order to evaluate performance of the control chart, two cases of equal shifts in both the stages and unequal shifts were considered and results were presented accordingly. The necessary measures are given to calculate the average run length (ARL) for shifted processes. The tables of ARLs are presented for equal and different sample sizes at first- and second- stage. Performance of the proposed control chart is presented using a simulation study
Kumaraswamy Esscher Transformed Laplace Distribution: Properties, Application and Extensions: Kumaraswamy Esscher Transformed Laplace Distribution
No full textIn this article, we introduce a new generalized family of Esscher transformed Laplace distribution, namely the Kumaraswamy Esscher transformed Laplace distribution. We study the various properties of the distribution including the survival function, hazard rate function, cumulative hazard rate function and reverse hazard rate function. The parameters of the distribution are estimated using the maximum likelihood method of estimation. A real application of this distribution on breaking stress of carbon fibres is also considered. Further, we introduce and study the exponentiated and transmuted exponentiated Kumaraswamy Esscher transformed Laplace distributions
Comparison of Infinite Capacity FM/FEk/1 Queuing Performance Using Fuzzy Queuing Model and Intuitionistic Fuzzy Queuing Model with Erlang Service Rates
No full textIn this work, we suggest an analytic technique with triangular fuzzy and triangular intuitionistic fuzzy numbers to compute the membership functions of considerable state-executing proportion in Erlang service models. The inter-entry rate, which is Poisson, and the admin (service) rate, which is Erlang, are both fuzzy-natured in this case, with FEk designating the Erlang probabilistic deviation with k exponentially phase. The numeric antecedents are shown to validate the model's plausibility, FM/FEk/1. A contextual inquiry is also carried out, comparing individual fuzzy figures. Intuitionistic fuzzy queueing models that are comprehensible are more categorical than fuzzy queueing models. Expanding the fuzzy queuing model to an intuitionistic fuzzy environment can boost the implementation of the queuing model. The purpose of this study is to assess the performance of a single server Erlang queuing model with infinite capacity using fuzzy queuing theory and intuitionistic fuzzy queuing theory. The fuzzy queuing theory model's performance evaluations are reported as a range of outcomes, but the intuitionistic fuzzy queuing theory model provides a myriad of values. In this context, the arrival and the service rate are both triangular and intuitionistic triangular fuzzy numbers. An assessment is made to find evaluation criteria using a design protocol in which fuzzy values are kept as they are and not made into crisp values, and two statistical problems are solved to understand the existence of the method
A Novel Accelerated Failure Time Model: Characterizations, Validation Testing, Different Estimation Methods and Applications in Engineering and Medicine
No full textIn this paper, we present a new exponential accelerated failure time model. Some of its properties and characterization results are derived. Different estimation methods are considered for assessing the finite sample behaviour of the estimators. Simulation studies for comparing the estimation methods are performed. Finally, we present a novel modified chi-square test for the novel exponential accelerated failure time model in both complete and right censored data cases. The validity of the new model is checked by using the theoretical global of the Nikulin-Rao-Robson. The maximum likelihood method is considered for this purpose. Two simulation studies are performed to assess the exponential accelerated failure time model and the efficiency of the Nikulin-Rao-Robson test statistic, respectively. Three real data sets are considered for illustrating the efficiency of the test statistic in validation
Estimation based on Ranked Set Sampling for Farlie--Gumbel--Morgenstern Bivariate Weibull Distribution Parameters with an application to medical data
No full textIn this article, we address the problem of estimating the parameters of Farlie-Gumbel-Morgenstern bivariate Weibull distribution using ranked set sample (RSS) design. The suggested estimators of the FGMBW distribution parameters are compared with their counterparts based on simple random sampling (SRS) via Monte Carlo simulations studies. An example of a real data set consists of times (in days) to the first and second recurrence of infection for 30 kidney patients is considered for illustration. It turns out that the RSS estimators results in an improvement in efficiency as compared to the simple random sampling estimators based on the same number of measured units for all cases considered in this study
GOLD DISTRIBUTION Another Look on the Generalization of Lindely Distribution
No full textIn this paper, a new generalization of one parameter Lindely distribution is proposed. The new distribution is a mixture distribution of Gamma distributions with fixed scale parameter and variable shape parameter. The distribution is called 'GOLD Distribution' as it is a generalization for several distributions such as exponential, Lindely, Sujatha, Amarendra, Devya and Shambhu distributions. The probability density and cumulative density functions are derived. Also, the statistical properties of the GOLD distribution are discussed. Parameter estimation using the maximum likelihood and the method of moments are given. Moreover, an illustration of the usefulness of the GOLD distribution in survival data analysis is discussed based on a real lifetime data
A New Inverse Kumaraswamy Family of Distributions: Properties and Application
No full textThe Kumaraswamy distribution is an important probability distribution used to model several hydrological problems as well as various natural phenomena whose process values are bounded on both sides. In this paper, we introduce a new family of inverse Kumaraswamy distribution and then explore its statistical properties. Conventional maximum likelihood estimators are considered for the parameters of this distribution and estimation based on dual generalized order statistics is outlined. A particular sub-model of this family; namely, the inverse Kumaraswamy- Weibull distribution is considered and some of its statistical properties are obtained. Estimation efficiency is numerically evaluated via a simulation study and two real-data applications of the proposed distribution are provided as well
Bayesian Inference for a Weighted Bilal Distribution: Regression Model
No full textIn this paper, a new lifetime distribution is proposed. Various statistical properties of the proposed distribution such as survival function, hazard rate function, mean residual life function, moments, moment generating function, Bonferroni curve, Lorenz curve, and order statistic are presented. The Bayesian estimator of the distribution parameter is derived. The behavior of the Bayesian estimator is assessed by a simulation study. Furthermore, a regression model is developed based on the proposed distribution. Some real data applications are analyzed to show the potentiality of the proposedmodels