Published

2017-01-16

Statistical properties and different methods of estimation of transmuted Rayleigh distribution

Propiedades estadísticas y diferentes métodos de estimación de la distribución de Rayleigh transmutada

DOI:

https://doi.org/10.15446/rce.v40n1.56153

Keywords:

Transmuted Rayleigh distribution, Hazard Rate Function, Conditional Moments, Order Statistics, Parameter Estimation (en)
Momentos distributivos, Estadísticas de orden, La estimación de parámetros, Riesgo de tipo de función, Rayleigh transmutada. (es)

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Authors

  • Sanku Dey Anthony´s College
  • Enayetur Raheem University of Northern Colorado
  • Saikat Mukherjee NIT Meghalaya
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.

Este artículo se aborda las varias propiedades y diferentes métodos para la estimación de los desconocidos parámetros de Transmuted Rayleigh (TR) distribución desde el punto de vista de un frequentist. Aunque la tema principal de este artículo es estimación, varias propiedades matemáticas y estadísticas de TR distribución (como cuantiles, momentos, una función que genera momentos, momentos condicionales, la tasa de peligro, la media vida residual, media vida pasada, la desviación media por media y mediana, organización stochastic, entropías varias, parámetros de tensión-fuerza y estadisticas de orden) están derivadas. Describimos brevemente los diferentes métodos de estimación, como máxima probabilidad, método de momentos, estimacién basada por percentil, mínimos cuadrados, método de máximos productos de espacios, el método de Cramér-von-Mises, los métodos de Anderson-Darling y right-tail Anderson-Darling, y compararlos con extensos estudios de simulaciones. Por último, la potencialidad del modelo está estudiando con dos conjuntos de datos reales. El margen de error, el promedio de error de las estimaciones y el percentage bootstrap de los confianza intervalos estan derivido por bootstrap remuestro.

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How to Cite

Dey, S., Raheem, E., & Mukherjee, S. (2017). Statistical properties and different methods of estimation of transmuted Rayleigh distribution. Revista Colombiana De Estadística, 40(1), 165-203. https://doi.org/10.15446/rce.v40n1.56153

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