Bayesian Estimation of Weighted Inverse Maxwell Distribution under Different Loss Functions (2025)

Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions

Heliyon, 2021

A three-parameter Maxwell-Mukherjee Islam distribution was proposed by applying Maxwell generalized family of distributions introduced by Ishaq and Abiodun [17]. The probability density and cumulative distribution functions of the proposed distribution were defined. The validity test was derived from its cumulative distribution function. The study aimed to obtain a Bayesian estimation of the scale parameter of Maxwell-Mukherjee Islam distribution by using assumptions of the Extended Jeffrey's (Uniform, Jeffrey's and Hartigan's), Inverse-Rayleigh and Inverse-Nakagami priors under the loss functions, namely, Squared Error Loss Function (SELF), Precautionary Loss Function (PLF) and Quadratic Loss Function (QLF), and their performances were compared. The posterior distribution under each prior and its corresponding loss functions was derived. The performance of the Bayesian estimation was illustrated from the basis of quantile function by using a simulation study and application to real life data set. For different sample sizes and parameter values, the QLF and SELF under Jeffrey's and Hartigan's priors produced the same estimates, bias and Mean Squared Error (MSE) just as we observed in their mathematical derivatives. Similarly, the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided the same performance when some parameter values are equal. For some parameter values, the QLF under Inverse-Nakagami and Inverse-Rayleigh priors produced the least values of MSE. In the application to real life data set, the QLF and SELF under Jeffrey's and Hartigan's priors; the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided similar results as observed in the simulation study. Therefore, the study concluded that the QLF under Inverse-Rayleigh and Inverse-Nakagami priors could effectively be used in the estimation of scale parameter of Maxwell-Mukherjee Islam distribution using Bayesian approach.

Bayesian Inference for Parameter and Reliability Function of Inverse Rayleigh Distribution Under Modified Squared Error Loss Function

2016

In this study, obtained some Bayes estimators based on Modified squared error loss function as well as Maximum likelihood estimator for scale parameter and reliability function of Inverse Rayleigh distribution. In order to get better understanding of our Bayesian analysis, we consider non-informative prior for the scale parameter using Jefferys prior information as well as informative prior density represented by Gamma distribution. Based on Monte-Carlo simulation study, the behavior of Bayes estimates of the scale parameter of inverse Rayleigh distribution have been compared depending on the mean squared errors (MSE’s), while the estimates of the reliability function have been compared depending on the Integrated mean squared errors (IMSE’s). In the current study, we observed that, the performance of Bayes estimator for the scale parameter and reliability function under Modified squared error loss function with Gamma prior is better than the corresponding estimators with Jefferys p...

Inverse Power Generalized Maxwell Distribution with Applications in Industry

Research Square (Research Square), 2023

Employing the inverse power transformation technique, we have proposed a new continuous threeparameter probability distribution and named it inverse power generalized Maxwell distribution. This distribution is the generalized version of the generalized Maxwell distribution. For this model, we have derived some functions related to survival analysis. Several statistical properties of the model are provided. This study also focused on the estimation of the unknown model parameters. Six different parameter estimation methods are employed and studied extensively through numerical simulation. To investigate the applications of the suggested model, two real engineering data sets are considered and empirically found that the suggested model can provide a superior fit as compared to some candidate models under study.

Parameter and reliability estimation of inverted Maxwell mixture model

Journal of Statistics and Management Systems, 2019

In present study the probability density function of mixture is derived for inverse Maxwell density. The main distributional properties and reliability characteristics are studied. Maximum likelihood estimation of the pertinent parameters along with failure rate functions and reliability are obtained. The Bayesian study of anonymous parameters of inverse Maxwell mixture model, assuming three priors is considered employed distinct loss functions. The prior reliance of mixture density is characterized by the inverted gamma, uniform and Jeffreys prior. The efficiencies of the considered set of estimates of mixture distribution parameters are studied through simulation. To scrutinize the response of prior reliance and loss functions posterior risks of the Bayes estimators are figured out and differentiated. Bayes estimator assuming the informative have been observed performing better.

Estimation of scale parameter of inverse gaussian distribution under a bayesian framework using different loss functions

Scientific Journal of Review, 2012

Bayesian Estimation for Exponentiated Inverted Weibull distribution under Different Loss Functions

IJOPAAR, 2019

The aim of the present article is to find the best estimator for the shape and scale parameter of exponentiated inverted Weibull distribution using informative and non-informative prior under squared error, linex and general entropy loss function. The performance of these proposed estimators has been compared on the basis of their simulated risk.

Beta inverse Maxwell Distribution with its Statistical Properties and Applications

JOURNAL OF SCIENTIFIC RESEARCH

The Maxwell distribution is one of the basic distributions in physics and commonly used to in statistical mechanics to determine the speed of molecules beside being popular in statistics for modeling life time data. In this article, we review the Beta Inverse Maxwell distribution and establish some statistical properties. We derive maximum likelihood estimator with confidence intervals.

Bayes Estimators for the Parameter of the Inverted Exponential Distribution under Symmetric and Asymmetric Loss Functions

This paper is devoted to discuss Bayes method to estimate the unknown scale parameter of the inverted exponential distribution along with the maximum likelihood method. Bayes estimators are obtained under symmetric "squared error" and asymmetric "precautionary" loss functions corresponding to informative "inverted gamma and Gumbel type II" and non-informative "Jeffrey and extension of Jeffrey" priors. The obtained Bayes estimators along with the maximum likelihood estimator are compared empirically for different cases and sample sizes using Monte-Carlo simulation method in terms of two statistical criteria which are mean squared error (MSE) and mean absolute percentage error (MAPE). Among the set of conclusions that have been reached, it is observed that, conjugate inverted gamma prior with hyper-parameters and record full appearance as best prior depending on the value of the parameter of inverted exponential distribution. Keywords: Inverted exponential distribution; maximum likelihood estimator; Bayes estimator; informative prior; non-informative prior; squared error loss function; precautionary loss function; mean squared error; mean absolute percentage error.

Parameter Estimation of Generalized Inverted Exponential Distribution via Bayesian Approach

Scholars Journal of Physics, Mathematics and Statistics, 2021

In this paper, generalized inverted exponential distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and AlBayyati’s loss functions by using quasi and gamma priors.

BAYESIAN ESTIMATION OF THE SHAPE PARAMETER OF THE GENERALISED EXPONENTIAL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

Pakistan Journal of Statistics and Operation Research, 2010

The generalized exponential (GE) distribution proposed by is an important lifetime distribution in survival analysis. In this article, we propose to obtain Bayes estimators and its associated risk based on a class of non-informative prior under the assumption of three loss functions, namely, quadratic loss function (QLF), squared log-error loss function (SLELF) and general entropy loss function (GELF). The motivation is to explore the most appropriate loss function among these three loss functions. The performances of the estimators are, therefore, compared on the basis of their risks obtained under QLF, SLELF and GELF separately. The relative efficiency of the estimators is also obtained. Finally, Monte Carlo simulations are performed to compare the performances of the Bayes estimates under different situations.