IJSREG Trion Studio

No Publication Cost

Vol 8, No 2:

openaccess

Power Transformation of Gamma-Rayleigh Distribution with Applications to Engineering Data
A A Bhat , S P Ahmad
Abstract
In this research paper, we have proposed a newthree parameter power Gamma-Rayleigh distribution, that is, a generalization of two parameter Gamma-Rayleigh distribution. Various mathematical properties of the proposed model such as moments, mean residual life, entropy and order statistics are acquired. The effect of the new parameter on the shape behavior of the density function has been discussed. The unknown parameters of the model have been estimated by employing the technique of maximum likelihood estimation. Finally, the practical importance of the model has been demonstrated by means of three real life data sets.
Full Text
PDF
References
A. R. El-Houssainy; W. A. Hassanein; T. A. Elhaddad; The Power Lomax distribution with an application to bladder cancer data, Springer Plus, 5 1838 (2016).
A. Renyi; On measures of entropy and information, Berkeley Symposium on Mathematical Statistics and Probability, 1(1) 547-561 (1960).
A. Zaka; A. S. Akhter; Methods for estimating the parameters of Power Function distribution, Pakistan Journal of Statistics and Operation Research, 9 213-224 (2013).
Alzaatreh; F. Famoye; C. Lee; The Gamma- Normal distribution: properties and applications, Computational Statistics and Data Analysis, 69 67-80 (2014).
C. Shannon; A mathematical theory of communication, Bell System Technical Journal, 27(3) 379-423 (1948).
D. Kundu; M. Z. Raqab; Generalized Rayleigh distribution: Different methods of estimations, Computational Statistics and Data Analysis, 49 187-200 (2005).
E. E. E. Akarawak; I. A. Adeleke; R. O. Okafor; The Gamma-Rayleigh Distribution and Applications to Survival Data, Nigerian Journal of Basic Applied Science, 25(2) 130-142 (2017).
E. J. Hannan; B. G. Quinn; The determination of the order of an auto regression, Journal of Royal Statistical Society: Series B, 41190-195 (1979).
F. Merovci; Transmuted Rayleigh distribution, Austrian Journal of Statistics, 42 (1) 21-31 (2013).
G. Schwarz; Estimating the dimensions of a model, The Annals of Statistics, 6(2) 461-464 (1978).
H. Akaike; A new look at the statistical model identification, IEEE Automatic Control, 19 716-723 (1974).
H. Bazdogan; Model selection and Akaike’s information criterion: The general theory and its analytical extensions, Psychometrika, 52 345-370 (1987).
J. Harvda; F. Charvat; Quantification method in classification processes: concept of structural entropy, Kybernetika, 3 30-35 (1967).
J. M. A. Nashaat; Estimation of two parameter powered inverse Rayleigh distribution, Pakistan Journal of Statistics, 36(2) 117-133 (2020).
K. K. Shukla; R. Shanker; Power Ishita distribution and its application to model lifetime data, Statistics in Transition, 19(1) 135-148 (2018).
M. D. Nichols; W. J. Padgett; A bootstrap control for Weibull percentiles, Quality and Reliability Engineering International, 22 141-151 (2006).
M. E. Ghitany; D. K. Al-Mutairi; N. Balakrishanan; L. J. Al-Enezi; Power Lindley distribution and associated inference, Computational Statistics and Data Analysis, 64 20-33 (2013).
M. E. Ghitany; D. K. Al-Mutairi; S. M. Aboukhamseen; Estimation of the reliability of a stress-strength system from power Lindley distributions, Communication in Statistics, Simulation and Computations, 44(1) 118-136 (2015).
M. G. Badar; A. M. Priest; Statistical aspects of fiber and bundle strength in hybrid composites, Hayashi, T., Kawata, K. and Umekawa, S. (eds), Progress in Science and Engineering Composites, ICCM-IV, Tokyo, 1129-1136 (1982).
M. H. Tahir; G. M. Cordeiro; M. Mansoor; M. Zubair; The Weibull-Lomax distribution: properties and applications, Hacettepe Journal of Mathematics and Statistics, 44(2) 461-480 (2015).
M. Nassar; S. Dey; Different estimation methods for Exponentiated Rayleigh distribution under constant-stress accelerated life test, Quality and Reliability Engineering International, 1-13 (2018).
M. W. A. Ramos; P. R. D. Marinho; R. V. Da Silva; G. M. Cordeiro; The exponentiated Lomax-Poisson distribution with an application to lifetime data, Advances Applications and Statistics, 34 107-135 (2013).
S. D. Krishnarani; On a Power Transformation of Half-Logistic distribution, Journal of Probability and Statistics, 5 1-10 (2016).
S. Mudasir; U. Jan; S. P. Ahmad; Weighted Rayleigh distribution revisited via informative and non-informative priors, Pakistan Journal of Statistics, 35(4) 321-348 (2019).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

Journal Content
Browser