Pakistan Journal of Statistics and Operation Research
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861 research outputs found
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A New Heavy-Tailed Exponential Distribution: Inference, Regression Model and Applications
No full textA new weighted exponentiated-exponential distribution is proposed to model financial data. It has heavy-tailed behavior which is suitable for data with right tails. Some actuarial measures for the new model are determined, and simulations are reported. Its parameters are estimated using nine approaches including a Bayesian method. A new Log-WEx-Exponential regression model is defined for right censored data. The importance of the new models is proved by applications to financial data
Modeling Real-life Data Sets with a Novel G Family of Continuous Probability Distributions: Statistical Properties, and Copulas
No full textThis work presents a novel two-parameter G family of continuous probability distributions with compounded parameters. To determine and examine the pertinent mathematical properties, calculations are performed. In one of the special sections, the standard inverse-Rayleigh baseline model is mathematically and statistically emphasized. We generated a number of bivariate and multivariate distributions using the copula method. These new distributions will aid in the modelling of bivariate and multivariate data. The applicability and flexibility of the new compounded two-parameters-G family are demonstrated through three applications to real-life data sets. These examples demonstrate the applicability of the family
Multimodal Alpha Skew Normal Distribution: A New Distribution to Model Skewed Multimodal Observations
No full textMultimodal alpha skew normal (MMASN) distribution is proposed for modelling skewed observations in the presence of multiple modality at arbitrary points. To this end the multimodal skew normal distribution of Chakraborty et al. (2015) is extended by integrating it with alpha skew normal distribution of Elal-Olivero (2010). Cumulative distribution function (cdf), moments, skewness and kurtosis of the proposed distribution are derived in compact form. The data modelling ability of the proposed distribution is checked by considering three multimodal data sets from literature in comparison to some nested and known distributions. Akaike Information Criterion (AIC) and the likelihood ratio (LR) test, both clearly favored proposed model over its nested models as expected
Approximate MLEs for the location and scale parameters of the Poisson-half-logistic distribution
No full textRecently, the application of compound distributions has increased due to the flexibility in fitting to actual data in various fields such as economics, insurance, etc. Poisson-half-logistic distribution is one of these distributions with an increasing-constant hazard rate that can be used in parallel systems and complementary risk models. Because of the complexity of the form of this distribution, it is not possible to obtain classical parameter estimates (such as MLE) by the analytical method for the location and scale parameters. We present a simple way of deriving explicit estimators by approximating the likelihood equations appropriately. This paper presents AMLE (Approximate MLE) method to obtain the location and scale parameters estimation. Using simulation, we show that this method is as efficient as the maximum likelihood estimators (MLEs), we obtain the variance of estimators from the inverse of the observed Fisher information matrix, and we see that when sample size increases bias and variance of these estimators, MSEs of parameters decrease. Finally, we present a numerical example to illustrate the methods of inference developed here
A new probability distribution: properties, copulas and applications in medicine and engineering
No full textIn this work, we construct a three-parameter Chen modification that is flexible. The "J shape", "monotonically increasing", "U shape," and "upside down (reversed bathtub)" hazard rate forms are all supported by the new Chen extension's hazard rate. We derive pertinent statistical features. A few distributions of the bivariate kind are generated. For evaluating the model parameters, we took the maximum likelihood estimation approach into consideration. Maximal likelihood estimators are evaluated via graphical simulations. To demonstrate the applicability of the new approach, two genuine data sets are taken into consideration and examined. The Akaike Information criterion, Bayesian Information criterion, Cramer-von Mises criterion, Anderson-Darling criterion, Kolmogorov-Smirnov test, and its related p-value are used to evaluate the new model with a variety of popular competing models
Modeling the Asymmetric Reinsurance Revenues Data using the Partially Autoregressive Time Series Model: Statistical Forecasting and Residuals Analysis
No full textThe autoregressive model is a representation of a certain kind of random process in statistics, insurance, signal processing, and econometrics; as such, it is used to describe some time-varying processes in nature, economics and insurance, etc. In this article, a novel version of the autoregressive model is proposed, in the so-called the partially autoregressive (PAR(1)) model. The results of the new approach depended on a new algorithm that we formulated to facilitate the process of statistical prediction in light of the rapid developments in time series models. The new algorithm is based on the values of the autocorrelation and partial autocorrelation functions. The new technique is assessed via re-estimating the actual time series values. Finally, the results of the PAR(1) model is compared with the Holt-Winters model under the Ljung-Box test and its corresponding p-value. A comprehensive analysis for the model residuals is presented. The matrix of the autocorrelation analysis for both points forecasting and interval forecasting are given with its relevant plots
Remarks on the Paper ”On the product and Quotient of Pareto and Rayleigh Random Variables”
No full textObeid and Kadry (2019) tried to study the product and quotient of the independent Pareto and Rayleigh random variables. The distributions they obtained are incorrect and in fact there is no closed form distributions as discussed here. We will mention the errors made and try to establish the correct versions of the probability density functions of these distributions for the truncated Pareto and Rayleigh random variables
A Class of Methods Using Interval Arithmetic Operations for Solving Multi–Objective Interval Transportation Problems
No full textThe objective of this article is studying on cost and time minimization of interval transportation problem (ITP) by using Best Candidate Method (BCM), Improved ASM method (IASM), ASM method, Zero Suffix Method (ZSM) and Zero Point Method (ZPM) with new interval arithmetic operations. We have obtained a better optimum result campared with existing methods available in the literature. The problems considered in this article are solved by the above listed methods without converting them into classical transportation problems. A comparative results are also given
Optimal Financial Resource Allocation Using Multiobjective Decision Making Model
No full textThe management of each industry must strive to meet multiple financial objectives, including capital structure, dividend policy, and earnings growth. The paper proposes an approach to analyze how financial resources should be allocated optimally using a multi-objective decision-making model. As part of the study, Al Rajhi banks' financial statements are used as a case study. All of the data is drawn from the banks' financial statements. Overall, the study's results show that all objectives have been achieved. This model enables banking and other industries to formulate strategies for dealing with various financial situations. The study's results are calculated and verified using LINGO 18.0 x64 software. Hence, the proposed model can determine financial decisions and develop strategies for dealing with various economic frameworks
Bayesian estimation for the type-I hybrid xgamma distribution using asymmetric loss function
No full textThis article proposes the Bayes estimation of the parameter and reliability function for xgamma distribution in the presence of type-I hybrid censored observations. The Bayes estimate of the parameter has been obtained by assuming informative and non-informative priors using general entropy loss function. Obviously, censoring adds difficulties in estimation procedure; hence the Bayes estimators computed with type-I hybrid censored observation under the mentioned prior often do not assume any standard form. Therefore, Bayes estimates are computed using Tierney-Kadane approximation and Markov Chain Monte Carlo numerical technique. Further, different interval estimates namely asymptotic confidence interval, bootstrap confidence interval and highest posterior density interval along with the width of the interval and coverage probability are also discussed. The maximum likelihood estimate for the same has also been computed using non- linear maximization iterative procedure and compared with corresponding Bayes estimates using Monte Carlo simulations. The comparison of the estimators are made in terms of average loss over whole sample space and corresponding length of the interval. lastly, one medical data set has been considered for the real application of the proposed study