International Journal of Statistics and Reliability Engineering

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Vol 8, No 1:

openaccess

MODIFIED HALF LOGISTIC WEIBULL DISTRIBUTION WITH STATISTICAL PROPERTIES AND APPLICATIONS

Govinda Prasad Dhungana , Vijay Kumar

Abstract

A new Modified Half Logistic Weibull (MHLW) distribution is developed in the type-I half logistic G family of distributions. The proposed model exhibits increasing, decreasing, and J-shaped & unimodal hazard function. In special case, this new model belongs to the half logistic distribution of type-II. Explicit expressions of reliability/ survival function, hazard rate function, reverse hazard rate function, cumulative hazard rate function; quantile function and median, mode; skewness, kurtosis; moments, residual life function, moment generating function; Rényi entropy and q-entropy; probability weighted moment and order statistics are investigated for the proposed MHLW distribution. The parameters of this distribution are estimated by maximum likelihood estimation. The asymptotic distributions of the estimators are also investigated. A simulation study has been performed to examine the behavior of maximum likelihood estimators. A real data set was used to show the applicability of MHLW distribution and noted that the proposed distribution provided a better fit as compared to some other known distributions.

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References

A. Garrido; R.Caro-Jesús; J. Octavio; A. Carnicero; M. Such; A new approach to fitting the three-parameter Weibull distribution: An application to glass ceramics, Communications in Statistics - Theory and Methods, 49(13)1-18(2019).

A. H. Soliman; M. A. E. Elgarhy; M. Shakil; Type II half logistic family of distributions with applications. Pakistan Journal of Statistics and Operation Research, 13(2) 245-264 (2017).

A. M. Almarashi; , M. Elgarhy; , M. Elsehetry; M. M. GolamKibria; B. M.; A. Algarni; A new extension of exponential distribution with statistical properties and applications. Journal of Nonlinear Sciences and Applications, 12 135-145 (2019).

A. M., Sarhan; M. Zaindin; Modified Weibull distribution. APPS. Applied Sciences, 11123-136(2019).

A. S. Hassan; M. Elgarhy; A new family of exponentiatedWeibull-generated distributions. International Journal of Mathematics and its Applications, 4(1) 135-148(2016).

A. S. Wahed; T. M. Luong; J. H. Jeong; A new generalization of Weibull distribution with application to a breast cancer data set. Statistics in medicine, 28(16) 2077-2094(2009).

B. S. El-Desouky; A. Mustafa; S. Al-Garash; The exponential flexible Weibull extension distribution. ArXivpreprint arXiv:1605.08152(2016)..

C. D. Lai; M. Xie; D. N. P. Murthy; A modified Weibull distribution. In IEEE Transactions on Reliability, 52(1) 33-37 (2003).

G. M. Cordeiro; M. Alizadeh; P.R. D. Marinho; The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, 86(4) 707-728 (2016).

G. S. Mudholkar; D. K. Srivastava; Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE transactions on reliability, 42(2) 299-302(1993).

M. A. UlHaq; R. M. Usman; S. Hashmi; A. I. Al-Omeri; The Marshall-Olkin length-biased exponential distribution and its applications. Journal of King Saud University-Science, 31(2) 246-251 (2019).

M. Anwar; A. Bibi; The half-logistic generalized Weibull distribution. Journal of Probability and Statistics, Hindawi; 1-18 (2018)..

M. Bebbington; C. D. Lai; R. Zitikis; A flexible Weibull extension. Reliability Engineering & System Safety, 92(6) 719-726 (2007).

M. Bourguignon, R.B. Silva; G. M. Cordeiro; The Weibull-G family of probability distributions. Journal of Data Science 12(1) 53-68 (2014).

M. D. Nichols; W. J. Padgett; A bootstrap control chart for Weibull percentiles. Quality and reliability engineering international, 22(2), 141-151(2006).

M. ElgarhyHaq; M. A.; I. Perveen; Type II Half Logistic Exponential Distribution with Applications. Annals of Data Science, 6(2) 245-257 (2019).

M. Mansoor; M. H. Tahir; G. M. Cordeiro; , S. B. Provost; A. Alzaatreh; The Marshall-Olkin logistic-exponential distribution. Communications in Statistics-Theory and Methods, 48(2) 220-234(2019).

M. Xie; Y. Tang; T.N. Goh; A modified Weibull extension with bathtub-shaped failure rate function, Reliability Engineering & System Safety, 76 279-285(2002).

N.Eugene; C. Lee; F. Famoye; Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31 497-512(2002).

R. Core; R. Team; A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URLhttps://www.R-project.org/ (2020).

R. D. Gupta; D. Kundu; Generalized exponential distribution: different method of estimations. Journal of Statistical Computation and Simulation, 69(4) 315-337 (2001).

S. K. Singh; U. Singh; A. S. Yadav; Bayesian estimation of Marshall–Olkin extended exponential parameters under various approximation techniques. Hacettepe Journal of Mathematics and Statistics, 43(2) 347-360 (2014).

S., Nadarajah; G. M. Cordeiro; E. M. Ortega; The exponentiated Weibull distribution: a survey. Statistical Papers, 54(3) 839-877 (2013).

V. Kumar; U. Ligges; A package for some probability distributions. http://cran.r-project.org/web/packages/reliaR/index.html (2011).

W. J. Braun; D. J. Murdoch; A first course in statistical programming with R. Cambridge University Press (2016).

Z. A. Al-saiary; R. A. Bakoban; A. A. Al-zahrani; Characterizations of the Beta Kumaraswamy. Exponential Distribution. Mathematics, 8(1) 23 (2020).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

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