Pakistan Journal of Statistics and Operation Research
Not a member yet
861 research outputs found
Sort by
A generating family of unit-Garima distribution: Properties, likelihood inference, and application
No full textThis article proposes the unit Garima (UGa) distribution for analysing proportion data. Some statistical properties of the UGa distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measure. Next, a new family of continuous distributions, called the unit Garima-generated (UGa-G) family of distributions, is studied. The UGa-G family of distributions has the feature to use the UGa distribution as the main generator and the concept of the T-X family of distributions. Some UGa-G family sub-models are provided, such as the UGa-Beta, UGa-Weibull, and UGa-normal distributions. The maximum likelihood method is used to estimate the model parameters for the statistical aspect. A Monte Carlo simulation for the percentile bootstrap confidence intervals for each parameter of the proposed distributions is provided. Applications to eight practical data sets are given to demonstrate the usefulness of the proposed distributions
A Bimodal Extension of the Tanh Skew Normal Distribution: Properties and Applications
No full textThis article introduces a novel family of skew distributions namely Bimodal Tanh Skew Normal (BTSN)distributions, which incorporates a new skew function with the help of hyperbolic tangent function. Thisnew distribution is designed to accommodate data sets with two modes. Besides, the article presents variousessential mathematical properties, such as moments, moment generating function, characteristic function,mean deviation, characterizations and the method for maximum likelihood estimation of this distribution.A simulation study is also conducted using Metropolis–Hastings algorithm to examine the behavior of theobtained parameters. Furthermore, the practical utility of this new distribution is demonstrated througha real life application involving a specific data set. To assess the suitability of the BTSN distribution, thearticle employs Akaike information criterion (AIC) and Bayesian information criterion (BIC). Finally, alikelihood ratio test is conducted to distinguish between the new model and the existing competing models
Approximation Methods for the Bivariate Compound Truncated Poisson Gamma Distribution
No full textIn certain situations probability computations are required for some complex distributions; like a compound distribution. This can leads to some comptational complexities. In such situations, the problem can be simplified by using some approximation techniques like the “saddle-point” approximation. In this paper, we have first proposed a compound bivariate distribution; namly the bivariate compound truncated Poisson-Gamma distribution; by compounding the zero truncated Poisson distribution with independent Gamma variates. The bivariate saddle-point approximation for the distribution function of the proposed distribution is obtained. An illustrative example for the approximate computation is given. An extensive simulatin study has been conducted to see the performance of the proposed saddle-point approximation for the distribution function of the bivariate compound truncated Poisson-Gamma distribution. It is found that the proposed saddle-point approximation is reasonably good to approximate the distribution function of the bivariate compound truncated Poisson-Gamma distribution
Dependence of Drought Characteristics: Parametric and Non-parametric Copula Approach
No full textDrought, which has harmful impacts both environmentally and economically, is one of the most devastating natural phenomena. In order to better understand and monitor the effects of drought, various methods have been developed in recent decades to quantify drought characteristics, with a primary focus on univariate drought indices. Mainly, drought characteristics are crucial to examine the impacts of drought in-depth on any specific area. This study endeavours to investigate univariate and bivariate drought indices using both parametric and non-parametric copula techniques. For that purpose, drought characteristics, such as duration, severity, mean intensity and peak intensity are analysed relying on different drought indices. The dependence among the main characteristics is evaluated and corresponding bivariate return period calculations are investigated. The data set used in this study is retrieved from monthly meteorological observations collected at five different Stations in Konya, located in the Central Anatolia Region of Turkey. Main numerical findings indicate the importance of using multiple drought indices for different geographical reasons for extreme dry periods
Estimation and Analysis of Trigonometric Models under Bayesian Approach
No full textIn this study, we explore three innovative trigonometric models within the Bayesian framework, utilizing the inverse Weibull distribution as our foundation. These models—namely the Sine inverse Weibull, Cosine inverse Weibull, and Tan inverse Weibull—are crafted from distinct distribution families. We employ both maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) simulation techniques to estimate parameters, drawing upon a comprehensive dataset. By scrutinizing posterior samples numerically and graphically, we evaluate the efficacy of our models, generating Bayes estimates for parameters, examining reliability and hazard functions, and establishing credible intervals. Furthermore, we assess the predictive capacity of all three models through posterior predictive checks. We also conduct comparative analyses, pitting our models against competing ones using real-world data. Notably, our results reveal that the proposed trio of models exhibit strikingly similar performance in terms of fitting the data
Generalized Exponential Ratio Type Estimator for the Finite Population Mean Under Ranked Set Sampling
No full textIn this study, we introduce a novel approach for estimating the mean of a finite population using Ranked Set Sampling (RSS), termed the generalized exponential ratio estimator. We derive expressions for the bias and mean squared error (MSE) of the proposed estimator up to the first order of approximation. To assess its performance, we conduct a thorough theoretical and numerical analysis using simulated and real data. Our results demonstrate that the generalized exponential ratio estimator outperforms both the classical ratio estimator and the estimator proposed by Kadilar et al. (2009) under RSS, highlighting its superior efficiency
A New Discrete Generator with Mathematical Characterization, Properties, Count Statistical Modeling and Inference with Applications to Reliability, Medicine, Agriculture, and Biology Data
No full textIn this piece of work, we examine and present a completely new discrete family of distributions that we have created. Our investigation into the relevant mathematical properties and characterizations of the system makes use of both analytical and numerical methods. We focus on a particular member of this family so that we can study its theoretical foundations as well as its graphical and numerical representations. This new model contains a few different hazard rate functions, some of which are referred to as "increasing constant", "decreasing-constant-increasing (U)", "constant", "U-constant", "decreasing", and "J-shape" In a similar vein, the model's probability mass function provides a variety of forms, all of which are helpful and practical. These forms include "asymmetric left skewed," "right skewed with wide peak," "right skewed," "bimodal," "symmetric," and "right skewed," amongst others. Each of these forms is valuable and applicable in their own way. These forms might be discovered in the probability mass function that the model generates. In this investigation, in addition to the Bayesian estimating technique under the traditional loss function of squared errors, we investigate and make use of a total of eight estimate strategies that are not founded on Bayesian theory (classical methods). Simulations employing the Markov Chain Monte-Carlo method are run for comparing the Bayesian way of estimation with the more traditional approach of estimating values. According to the findings that we've compiled, the estimation strategy that is referred to as maximum likelihood yields the most accurate results across the board and for all different types of sample sizes. In addition, we evaluate and contrast the various methods of estimation by making use of six distinct real dataset sets; this indicates the versatility of the unique model that we have developed
Flexible Group Service MAP/ PH/ 1 Queueing Model with Working Breakdown, Repair and Balking
No full textIn reality, there are many uses of queues where services are provided in groups and these type of queues are widely studied in the literature. In this paper we examine a particular queueing model, wherein the services are provided in groups ranging from 1 to a pre defined constant, denoted as K, and the arrival follows a Markovian arrival process. The service time of each individual customer follows phase type distribution. The maximum of each customers individual service time within a group is defined as the group's service time. At the service completion moment if there are fewer customers than K, the server won't begin the subsequent service until the system's customer size reaches K or a randomly assigned admission period expires, whichever happens first. The phase type representation of the service times depends on the group's size. Anytime a server breakdowns and it will not proceed to repair, instead it will serve the affected customer group at a slower pace. After that specific customer group's service is finished, the server will immediately undergo repair to fix any issues. The process of repair and breakdown occurs at exponential rate. When the server breakdowns, the customer might balk. The Markov chain's stability condition is determined and stationary probability vector is computed. Formulas for the primary system performance measures are given. Numerical and graphical representations of the proposed model are illustrated
A new bathtub and increasing failure rate model: An extension of the Mustapha type II distribution
No full textThis article introduces a new three-parameter lifetime model with an increasing and bathtub failure rate functions as an extension of the Mustapha type II distribution (MuII). The model can be very useful in statistical studies, reliability, computer sciences and engineering. Various mathematical and statistical properties of the distribution are discussed, such as moments, mean deviations, Bonferroni and Lorenz curves, entropy, order statistic, and extreme value distributions. Moreover, we consider the bivariate extension of the new model. Statistical inferences by the maximum likelihood method are discussed and assess by simulation studies. Applications of the proposed model to two right-skewed data are presented for illustration. The new model provides a better fit than some other existing distribution as measured by some model selection criteria and goodness of fits statistics
Approximations to the Moments of Order Statistics for Normal Distribution
No full textOrder statistics occupy an important place in statistical theory. They have an important place in many fields of applied statistics such as goodness of fit tests and parameter estimation. In addition, it is necessary to find the expected values of these order statistics in these application areas. However for some probability distributions, these expected values are very difficult to find such as the standard normal distribution. So the problem of finding the expected values of the order statistics in statistical theory is of importance. In this study, two novel approximation methods are proposed for the expected values of the order statistics of the standard normal distribution. Also, the true values with previously given approximations, simulation results and our proposed approximations are compared by using mean square error (MSE), mean absolute error (MAE) and maximum error (ME) criteria. Furthermore, to evaluate the performances of all approximation methods, we compute the differences between exact values and approximation values. Then, the plot of these differences against the exact values is given. Based on both the plots and the comparison results, novel approximations fit the true values better than the other approximations presented in this paper