A Unified Approach for Generalizing Some Families of Probability Distributions, with Applications to Reliability Theory

Ahmed A. Fattah, A-Hadi N. Ahmed

Abstract


In this paper, we propose a new method for generating families of continuous distributions based on the star-shaped property which grantees the existences of some well know properties for the generated classes and distributions for any non-negative random variables. We refer to the new class as the composed  family or shortly ( ) family. We study some mathematical properties of the new family. Some special families and sub-models of it from the  family are discussed. To examine the performance of our new family and the generated models in fitting several data we use two real sets of data; censored and uncensored then comparing the fitting of a new produced model called composed- Lomax Weibull  with some well-known models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples.

Keywords


Star Shaped, Survival Function, Moment Generating Function, Inversion Method

Full Text:

PDF


DOI: http://dx.doi.org/10.18187/pjsor.v14i2.2219

Refbacks

  • There are currently no refbacks.




Copyright (c) 2018 Pakistan Journal of Statistics and Operation Research

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Title

A Unified Approach for Generalizing Some Families of Probability Distributions, with Applications to Reliability Theory

Keywords

Star Shaped, Survival Function, Moment Generating Function, Inversion Method

Description

In this paper, we propose a new method for generating families of continuous distributions based on the star-shaped property which grantees the existences of some well know properties for the generated classes and distributions for any non-negative random variables. We refer to the new class as the composed  family or shortly ( ) family. We study some mathematical properties of the new family. Some special families and sub-models of it from the  family are discussed. To examine the performance of our new family and the generated models in fitting several data we use two real sets of data; censored and uncensored then comparing the fitting of a new produced model called composed- Lomax Weibull  with some well-known models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples.

Date

2018-06-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 14 No. 2, 2018



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810