1 Prediction Distribution of Generalized Geometric Series Distribution and Its Different Forms (original) (raw)

PREDICTION DISTRIBUTION OF GENERALIZED GEOMETRIC SERIES DISTRIBUTION AND ITS DIFFERENT FORMS

The prediction distribution of generalized geometric series distribution (GGSD) and of its truncated and size-biased forms is derived and studied under the non-informative and beta prior distributions. The prediction distributions for all the models are beta distribution, but the parameters of the prediction distributions depend on the choice of the prior distribution as well as the model under consideration.

On size-biased generalized logarithmic series distribution

Studia Scientiarum Mathematicarum Hungarica, 2009

In this paper a size-biased generalized logarithmic series distribution (SBGLSD), a particular case of the weighted generalized logarithmic series distribution, taking the weights as the variate values is defined. The moments and recurrence relation of SBGLSD are obtained. We have also established the relationship between the moments of size-biased generalized logarithmic series distribution and size-biased generalized geometric series distribution (SBGGSD). Bayesian estimation of SBGLSD is discussed and a comparison is made with the generalized logarithmic series distribution (GLSD) by using the Monte Carlo simulation technique.

A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

2021

In this paper, a new modified version of geometric distribution is proposed. The newly introduced model is called transmuted record type geometric (TRTG) distribution. TRTG distribution is a good alternative to the negative binomial, Poisson and geometric distributions in modeling real data encountered in several applied fields. The main statistical properties of the new distribution were obtained. We determined the measures of value at risk and tail value at risk for the TRTG distribution. These measures are important quantities in actuarial sciences for portfolio optimization under uncertainty. The TRTG parameters were estimated via maximum likelihood, moments, proportions, and Bayesian estimation methods, and the simulation results were determined to explore their performance. Furthermore, a new count regression model based on the TRTG distribution was proposed. Four real data applications were adopted to illustrate the applicability of the TRTG distribution and its count regress...

A new compounding family of distributions: The generalized gamma power series distributions

Journal of Computational and Applied Mathematics, 2016

We propose a new four-parameter family of distributions by compounding the generalized gamma and power series distributions. The compounding procedure is based on the work by Marshall and Olkin (1998) and defines 76 sub-models. Further, it includes as special models the Weibull power series and exponential power series distributions. Some mathematical properties of the new family are studied including moments and generating function. Three special models are investigated in details. Maximum likelihood estimation of the unknown parameters for complete sample is discussed. Two applications of the new models to real data are performed for illustrative purposes.

Exponentiated Half Logistic-Generalized G Power Series Class of Distributions: Properties and Applications

Journal of Probability and Statistical Science

A new generalized class of distributions called the Exponentiated Half Logistic-Generalized G Power Series (EHL-GGPS) distribution is proposed. We present some special cases in the proposed distribution. Several mathematical properties of the EHL-GGPS distribution were also derived including order statistics, moments and maximum likelihood estimates. A simulation study for selected parameter values is presented to examine the consistency of the maximum likelihood estimates. Finally, some real data applications of the EHL-GGPS distribution are presented to illustrate the usefulness of the proposed class of distributions.

The Odds Generalized Gamma-G Family of Distributions: Properties, Regressions and Applications

2020

In this article, a new "odds generalized gamma-G" family of distributions, called the GG-G family of distributions, is introduced. We propose a complete mathematical and statistical study of this family, with a special focus on the Frechet distribution as baseline distribution. In particular, we provide infinite mixture representations of its probability density function and its cumulative distribution function, the expressions for the Renyi entropy, the reliability parameter and the probability density function of ith order statistic. Then, the statistical properties of the family are explored. Model parameters are estimated by the maximum likelihood method. A regression model is also investigated. A simulation study is performed to check the validity of the obtained estimators. Applications on real data sets are also included, with favorable comparisons to existing distributions in terms of goodness-of-fit.

A generalized geometric distribution and some of its properties

Statistics & Probability Letters, 1983

A generalized geometric distribution is introduced and briefly studied. First it is noted that it is a proper probability distribution. Then its probability generating function, mean and variance are derived. The probability distribution of the sum Y, of r independent random variables, distributed as generalized geometric, is derived. Finally, sufficient conditions are presented under which we can derive the limiting distribution of Y, -kr as r ~ o0.

A New Method of Estimation of Size-Biased Generalized Logarithmic Series Distribution

The Open Statistics & Probability Journal, 2009

In this paper, a size-biased generalized logarithmic series distribution (SBGLSD) is introduced and its moments are obtained. The estimates of the parameters of SBGLSD are obtained by employing the method of moments and a proposed new method of estimation. The new proposed method of estimation uses the non-zero frequency of a variable only up to a finite value. In this method, the estimation of only one parameter is needed and of the other is obtained by the relationship among the parameters by counting the number of non-zero frequency classes. The method is found very simple and quick to apply in practice. Extensive simulations are performed to compare the performances of the proposed and the moment method of estimation mainly with respect to their biases and mean squared errors (MSE's), for different sample sizes and of different parametric values. Comparison has been made among different estimation methods by means of Pearson's Chi-square, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) techniques.

The Modified Power Series Inverted Exponentiated Generalized Class of Distributions: Statistical Measures, Model Fit, and Characterization

Earthline Journal of Mathematical Sciences, 2020

Within the master thesis [1], the author considered the following random variable T=X^{-1}-1,$$ where XXX follows the Kumaraswamy distribution, and obtains a so-called inverted Kumaraswamy distribution, and studies some properties and applications of this class of distributions in the context of the power series family [2]. Within the paper [3], they introduced the exponentiated generalized class of distributions and obtained some properties with applications. Based on these developments we introduce a class of modified power series inverted exponentiated generalized distributions and obtain some of their properties with applications. Some characterization theorems are also presented. Avenues for further research concludes the paper.