New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications

Omid Shojaee; Reza Azimi

Applications of Mathematics (2025)

  • Issue: 2, page 231-256
  • ISSN: 0862-7940

Abstract

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Fitting a suitable distribution to the data from a real experiment is a crucial topic in statistics. However, many of the existing distributions cannot account for the effect of environmental conditions on the components under test. Moreover, the components are usually heterogeneous, meaning that they do not share the same distribution. In this article, we aim to obtain a new generalization of the Compound Rayleigh distribution by using mixture models and incorporating the environmental conditions on the components. The new distribution is expected to be a flexible distribution that encompasses some other distributions as special cases. We will also examine the properties and aging criteria of the new distribution. Over the past decades, various methods to estimate the unknown parameters of a statistical distribution have been proposed from the availability of type-II censored data. Thus, we estimate the parameters of the proposed distribution in the presence of type-II censored data using a Monte Carlo simulation study and real data analysis with maximum likelihood, maximum product of spacings, and Bayesian methods. Finally, different methods are compared by calculating the mean square error (MSE) of the resulting estimators.

How to cite

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Shojaee, Omid, and Azimi, Reza. "New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications." Applications of Mathematics (2025): 231-256. <http://eudml.org/doc/299986>.

@article{Shojaee2025,
abstract = {Fitting a suitable distribution to the data from a real experiment is a crucial topic in statistics. However, many of the existing distributions cannot account for the effect of environmental conditions on the components under test. Moreover, the components are usually heterogeneous, meaning that they do not share the same distribution. In this article, we aim to obtain a new generalization of the Compound Rayleigh distribution by using mixture models and incorporating the environmental conditions on the components. The new distribution is expected to be a flexible distribution that encompasses some other distributions as special cases. We will also examine the properties and aging criteria of the new distribution. Over the past decades, various methods to estimate the unknown parameters of a statistical distribution have been proposed from the availability of type-II censored data. Thus, we estimate the parameters of the proposed distribution in the presence of type-II censored data using a Monte Carlo simulation study and real data analysis with maximum likelihood, maximum product of spacings, and Bayesian methods. Finally, different methods are compared by calculating the mean square error (MSE) of the resulting estimators.},
author = {Shojaee, Omid, Azimi, Reza},
journal = {Applications of Mathematics},
keywords = {Bayesian estimation; compound Rayleigh distribution; maximum likelihood; maximum product of spacings; Monte Carlo simulation; Rayleigh distribution},
language = {eng},
number = {2},
pages = {231-256},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications},
url = {http://eudml.org/doc/299986},
year = {2025},
}

TY - JOUR
AU - Shojaee, Omid
AU - Azimi, Reza
TI - New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 2
SP - 231
EP - 256
AB - Fitting a suitable distribution to the data from a real experiment is a crucial topic in statistics. However, many of the existing distributions cannot account for the effect of environmental conditions on the components under test. Moreover, the components are usually heterogeneous, meaning that they do not share the same distribution. In this article, we aim to obtain a new generalization of the Compound Rayleigh distribution by using mixture models and incorporating the environmental conditions on the components. The new distribution is expected to be a flexible distribution that encompasses some other distributions as special cases. We will also examine the properties and aging criteria of the new distribution. Over the past decades, various methods to estimate the unknown parameters of a statistical distribution have been proposed from the availability of type-II censored data. Thus, we estimate the parameters of the proposed distribution in the presence of type-II censored data using a Monte Carlo simulation study and real data analysis with maximum likelihood, maximum product of spacings, and Bayesian methods. Finally, different methods are compared by calculating the mean square error (MSE) of the resulting estimators.
LA - eng
KW - Bayesian estimation; compound Rayleigh distribution; maximum likelihood; maximum product of spacings; Monte Carlo simulation; Rayleigh distribution
UR - http://eudml.org/doc/299986
ER -

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