New Mathematical Properties For Rayleigh distribution

Authors

  • Rehab Mahmoud Cairo University
  • Salah M. Mohamed Cairo University

DOI:

https://doi.org/10.20956/j.v19i1.21946

Keywords:

Harmonic Mean, Moment Generating Function, Characteristic Function, Quantile function, Raw Moments, Moments of Residual life (MRL)

Abstract

Regression analysis is one of the most commonly statistical techniques used for analyzing data in different fields. And used to fit the relation between the dependent variable and the independent variables require strong assumption to be met in the model. Generalized linear models (GLMs) allow the extension of linear modeling ideas to a wider class of response types, such as count data or binary responses. Many statistical methods exist for such data types, but the advantage of the GLM approach is that it unites a seemingly disparate collection of response types under a common modeling methodology. So, the problem of the current research is to try to provide a new mathematical property for Exponentiated Rayleigh distribution, and it was one of the most important properties that was studied is to determine Harmonic Mean, as well as calculating the Quantile function, Moments of Residual life (MRL), Reversed Residual Life, Mean of Residual life. The study also presented the probability density function (pdf) and cumulative distribution function according to linear representations.  

Downloads

Download data is not yet available.

References

Bhat, A. A., & Ahmad, S. P., 2020. A NEW GENERALIZATION OF RAYLEIGH DISTRIBUTION: PROPERTIES AND APPLICATIONS. Pakistan journal of statistics, 36(3).‏

Cordeiro, G. M., Rodrigues, G. M., Ortega, E. M., de Santana, L. H., & Vila, R., 2022. An extended Rayleigh model: Properties, regression and COVID-19 application. arXiv preprint arXiv:2204.05214.‏

Cordeiro, G.M., de Azevedo Cysneiro, F.J., and Cabral, P.C., 2021b. Estat´ısticas B´asicas e Modelagem de Regress˜ao das taxas de mortalidade por COVID-19 nos Estados Brasileiros. Brazilian Journal of Development, 72, 117735-117749.

Cordeiro, G.M., Figueiredo, D., Silva, L., Ortega, E.M.M., and Prataviera, F., 2021a. Explaining COVID-19 mortality rates in the first wave in Europe. Model Assisted Statistics and Applications, 16, 211-221.

Figueroa-Zuniga, J.I., Niklitschek, S., Leiva, V., Liu, S., 2021. Modeling heavy-tailed bounded data by the trapezoidal beta distribution with applications. Revstat 2021, in press.

Greene WH, Econometric Analysis. 7th edition. Pearson.

Henningsen, A., 2011. censReg: Censored Regression (Tobit) Models. R package version 0.5, http://CRAN.R-project.org/package=censReg.

Mace III, M. M., & Wilberg, M. J., 2020. Using censored regression when estimating abundance with CPUE data to account for daily catch limits. Canadian Journal of Fisheries and Aquatic Sciences, 77(4), 716-722.‏

Mazucheli, J., Leiva, V., Alves, B., & Menezes, A. F., 2021. A new quantile regression for modeling bounded data under a unit Birnbaum–Saunders distribution with applications in medicine and politics. Symmetry, 13(4), 682.‏

Menezes, A.F.B., Mazucheli, J., 2021. Bourguignon, M. A parametric quantile regression approach for modelling zero-or-one inflated double bounded data. Biometr. J. 2021, 63, 841–858. [CrossRef] [PubMed]

Moors, J. J. A., 1988. A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 37(1), 25-32.

Mudasir, S., Jan, U. and Ahmad, S.P., 2019. Weighted Rayleigh distribution revisited via informative and non-informative priors. Pakistan Journal of Statistics, 35(4), 321-348

Ogunsanya A. S., Sanni O.O. M.and Yahya W. B., 2019. Exploring Some Properties of Odd Lomax-Exponential Distribution. Annals of Statistical Theory and Applications (ASTA) 1: 21-30.

Ogunsanya, A. S., Akarawak, E. E., & Ekum, M. I., 2021. On some properties of Rayleigh-Cauchy distribution. Journal of Statistics and Management Systems, 24(6), 1213-1231.‏

Shukla, K.K. and Shanker, R., 2018. Power Ishita distribution and its application to model lifetime data. Statistics in Transition, 19(1), 135-148.

Downloads

Published

2022-09-07

Issue

Section

Research Articles