The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

被引:45
作者
Almarashi, Abdullah M. [1 ]
Elgarhy, Mohammed [2 ]
Jamal, Farrukh [3 ]
Chesneau, Christophe [4 ]
机构
[1] King AbdulAziz Univ, Fac Sci, Stat Dept, Jeddah 21551, Saudi Arabia
[2] Valley High Inst Management Finance & Informat Sy, Obour 11828, Qaliubia, Egypt
[3] Govt SA Postgrad Coll Dera Nawab Sahib, Dept Stat, Bahawalpur 63100, Punjab, Pakistan
[4] Univ Caen, LMNO, Dept Math, Campus 2,Sci 3, F-14032 Caen, France
来源
SYMMETRY-BASEL | 2020年 / 12卷 / 04期
关键词
truncated family of distributions; inverse Weibull distribution; moments; order statistics; maximum likelihood method; simulation; data analysis;
D O I
10.3390/sym12040650
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, we propose a generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter. We motivate this generalization by presenting theoretical and practical gains, both consequences of new flexible symmetric/asymmetric properties in a wide sense. Our main mathematical results are about stochastic ordering, uni/multimodality analysis, series expansions of crucial probability functions, probability weighted moments, raw and central moments, order statistics, and the maximum likelihood method. The special member of the family defined with the inverse Weibull distribution as baseline is highlighted. It constitutes a new four-parameter lifetime distribution which brightensby the multitude of different shapes of the corresponding probability density and hazard rate functions. Then, we use it for modelling purposes. In particular, a complete numerical study is performed, showing the efficiency of the corresponding maximum likelihood estimates by simulation work, and fitting three practical data sets, with fair comparison to six notable models of the literature.
引用
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页数:21
相关论文
共 48 条
[1]  
Abid S. H., 2017, Applied Mathematics, V7, P51, DOI 10.5923/j.am.20170703.03
[2]   On the Generalized Inverse Weibull Distribution [J].
Abid, Salah Hamza ;
Al-Noor, Nadia Hashim ;
Boshi, Mohammad Abd Alhussein .
INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2018), 2019, 2086
[3]  
Ahmad M., 2007, INT J STAT SCI, V6, P43
[4]  
Aldahlan M.A., 2019, Int. J. Math. Its Appl, V7, P221
[5]   The Truncated Cauchy Power Family of Distributions with Inference and Applications [J].
Aldahlan, Maha A. ;
Jamal, Farrukh ;
Chesneau, Christophe ;
Elgarhy, Mohammed ;
Elbatal, Ibrahim .
ENTROPY, 2020, 22 (03)
[6]   Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications [J].
Aldahlan, Maha A. ;
Jamal, Farrukh ;
Chesneau, Christophe ;
Elbatal, Ibrahim ;
Elgarhy, Mohammed .
PLOS ONE, 2020, 15 (03)
[7]   Log-gamma-generated families of distributions [J].
Amini, Morteza ;
MirMostafaee, S. M. T. K. ;
Ahmadi, J. .
STATISTICS, 2014, 48 (04) :913-932
[8]  
[Anonymous], 2014, AUST J BASIC APPL SC
[9]  
[Anonymous], WEIBULL DISTRIBUTION
[10]  
[Anonymous], 2019, SYMMETRY BASEL, DOI DOI 10.3390/SYM11111410