Statistical properties and different methods of estimation of transmuted Rayleigh distribution

This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view,  yet, various mathematical and statis...

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Autores:
Dey, Sanku
Raheem, Enayetur
Mukherjee, Saikat
Tipo de recurso:
Article of journal
Fecha de publicación:
2017
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66508
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66508
http://bdigital.unal.edu.co/67536/
Palabra clave:
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Transmuted Rayleigh distribution
Hazard Rate Function
Conditional Moments
Order Statistics
Parameter Estimation
Momentos distributivos
Estadísticas de orden
La estimación de parámetros
Riesgo de tipo de función
Rayleigh transmutada.
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
Description
Summary:This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view,  yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments,  hazard rate, mean residual lifetime, mean past lifetime,  mean deviation about mean and median, the stochastic ordering,  various entropies, stress-strength parameter  and order statistics) are derived.  We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings,  method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.