Bayesian estimation using Lindley’s approximation of Inverted Kumaraswamy distribution based on lower record values

In this paper, we have considered estimation of unknown parameters based on lower record values for Inverted Kumaraswamy distribution. Maximum likelihood and approximate Bayes estimators based on lower record values for unknown parameters of this distribution are obtained. Lindley’s approximation (L-approximation) is used to obtain approximate Bayes estimators under DeGroot loss function based on lower record values. A Simulation study and a real data analysis are presented to illustrate the results.Publisher's Versio

Comparison on the Bayesian Estimation of Gompertz Distribution Based on Type I Censored Data

The paper depicts assessment of the Bayesian methodology utilizing Gaussian quadrature formulas and Markov Chain Monte Carlo of the Gompertz distribution based on type I censored data with two loss functions, the Square Error loss function and the Linear Exponential loss function. In Markov Chain Monte Carlo, the full conditional distributions for the scale and shape parameters, survival and hazard functions are acquired by means Gibbs sampling and Metropolis- Hastings algorithm. The strategies for the Bayesian methodology are contrasted with maximum likelihood estimation regarding the Mean Square Error (MSE) to decide the best assessing of the scale and shape parameters, survival and hazard functions of the Gompertz distribution based on type I censored data. Keywords: Gompertz distribution, Bayesian estimation, Type I censored data, Gaussian Quadrature Formulas, Markov Chain Monte Carlo

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Gompertz and Gamma Gompertz Distributions

In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODE) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the Gompertz and gamma Gompertz distributions. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distributions. Solutions of these ODEs by using numerous available methods are a new ways of understanding the nature of the probability functions that characterize the distributions. The method can be extended to other probability distributions and can serve an alternative to approximation especially the cases of the quantile and inverse survival functions. Finally, the link between distributions extended to their differential equations as seen in the case of the ODE of the hazard function of the gamma Gompertz and exponential distributions

On Bayesian Estimation and Predictions for Two-Component Mixture of the Gompertz Distribution

Mixtures models have received sizeable attention from analysts in the recent years. Some work on Bayesian estimation of the parameters of mixture models have appeared. However, the were restricted to the Bayes point estimation The methodology for the Bayesian interval estimation of the parameters for said models is still to be explored. This paper proposes the posterior interval estimation (along with point estimation) for the parameters of a two-component mixture of the Gompertz distribution. The posterior predictive intervals are also derived and evaluated. Different informative and non-informative priors are assumed under a couple of loss functions for the posterior analysis. A simulation study was carried out in order to make comparisons among different point and interval estimators. The applicability of the results is illustrated via a real life example

Inference for exponentiated general class of distributions based on record values

<p>The main objective of this paper is to suggest and study a new exponentiated general class (EGC) of distributions. Maximum likelihood, Bayesian and empirical Bayesian estimators of the parameter of the EGC of distributions based on lower record values are obtained. Furthermore, Bayesian prediction of future records is considered. Based on lower record values, the exponentiated Weibull distribution, its special cases of distributions and exponentiated Gompertz distribution are applied to the EGC of distributions.  </p

Random Number Generators

The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution’s characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit