¹St. Anthony's College, Department or Statistics, Shillong, India. PhD. Email: sanku_dey2k2003@yahoo.co.in
²University of Northern Colorado, Applied Statistics and Research Methods, Greeley, USA. PhD. Email: enayetur.raheem@unco.edu
³NIT Meghalaya, Shillong, India. PhD. Email: saikat.mukherjee@nitm.ac.in

This article addresses various properties and different methods of estimation of the unknown Transmuted Rayleigh (TR) distribution parameters from a frequentist point of view. Although our main focus is on estimation, 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 methods of estimation such as maximum likelihood, method of moments, percentile based estimation, least squares, method of maximum product of spacings, method of Cramér-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling, and compare them using extensive simulations studies. Finally, the potentiality of the model is studied using two real data sets. Bias, standard error of the estimates, and bootstrap percentile confidence intervals are obtained by bootstrap resampling.

Key words: Distributional Moments, Order Statistics, Parameter Estimation; Rate Risk Function, Rayleigh Distribution, Transmuted Rayleigh Distribution.

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.

Palabras clave: momentos distributivos, estadísticas de orden, la estimación de parámetros, riesgo de tipo de función, rayleigh transmutada.

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