Type II Topp-Leone Dagum distribution for modeling failure times data
Downloads
Abstract
In this paper, we introduce four parameter continuous probability distribution and named it as Type II Topp-Leone
Dagum distribution which is generated using Type II Topp-Leone generated family of distributions. We observe
different desirable properties of Type II Topp-Leone Dagum distribution. We present expressions for important
statistical measures such as moments, moment generating function, cumulant generating function, inverted
moments, probability weighted moments, reliability function, hazard rate function, reversed hazard function,
cumulative hazard function, second failure rate function, mean waiting time, mean residual life, Bonferroni index,
Lorenz curve and generalized entropy. For the proposed distribution, the parameters of the distribution are
estimated by using maximum likelihood method. Finally, we used failure time of air conditioners data to study
performance of the proposed distribution.
Keywords:
Type II Topp-Leone generated family,, Dagum distribution,, Generalized entropy,, Probability weighted moment,, Maximum likelihood estimation.Mathematics Subject Classification:
Mathematics- Pages: 343-353
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
C. Bonferroni, Elmenti di statistica generale. Libreria Seber, Firenze.(1930).
F.A. Cowell, On the structure of additive inequality measures, The Rev. of Eco.Stud., 47(1980), 521-531.
G. M. Cordeiro, M. De Castro, A new family of generalized distributions, Jour. of Stat. and Comp. Simu., 81(2009), 883-893.
C. Dagum, A new model of personal income distribution: specification and estimation, Eco. Appli., 30(1977), 413437.
C. Dagum, The generation and distribution of income, the Lorenz curve and the Gini ratio, Eco. Appli., 33(1980), 327-367.
F. Domma, Landamento della Hazard function nel modello di Dagum a treparametri, Quaderni di Statistica., $4(2002), 103-114$.
F. Domma, S. Giordano and M. Zenga, Maximum Likelihood Estimation in Dagum distribution from Censored Samples, J.of Appl. Stat., 38(2011), 2971-2985.
I. Elbatal, G. Aryal, Transmuted Dagum Distribution, Chile. J. of Stati., 2(2015), 31-45.
M. Elgarhy, M. Arslan Nasir, Farrukh Jamal, and Gamze Ozel, The type II Topp-Leone generated family of distributions: Properties and application, J. of stat. and mana. syst., (2018), 1529-1551.
R. C. Gupta, P. L. Gupta, and R. D. Gupta, Modeling failure time data by Lehmann alternatives, Com. in Stat. Theory and Methods., 27(1998), 887-904.
A.S. Hassan, M. Elgarhy, A new family of exponentiated Weibull-generated distributions, Inter J. of Mat. and its Appl., 4(2016), 135-148.
S. Huang and B.O. Oluyede, Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data, J.of Stat. Distr. and Appli., (2014), 1-20.
C. Kleiber and Kotz, Statistical Size Distribution in Economics and Actuarial Sciences, new York: John Wiley and Sons Inc,(2003).
C. Kleiber, A guide to the Dagum distribution: Duangkamon, C.Modeling Income Distributions and Lorenz Curves Series: Economic Studies in Inequality, Social Exclusion and Well-Being, 5(2008), Springer, New York.
M.O. Lorenz, Methods of measuring the concentration of wealth, Amer. Stat. Assoc., 9(1905), 209-219.
F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics., 5(1963), 375-383.
G. Pietra, Della relazioni fra indici di variability, not I e II. Atti del Reale Istituto Veneto di Scienze, it Lettereed Arti., 74(1915), 775-804.
W. Shaw, I. Buckley, The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skewkurtotic-normal distribution from a rank transmutation map, arXiv:(2009), 0901-0434.
C. W. Topp, F. C. Leone, A family of J-shaped frequency functions, J. of the Amer. Stat. Assoc., 50(1955), 209-219.
M. Zenga, La curtosi (Kurtosis), Statistica., 56(1996), $87-101$
Similar Articles
- Prasanta Malik, Samiran Das, $\mathscr{I}_\lambda$-statistical limit points and $\mathscr{I}_\lambda$-statistical cluster points , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
