1
|
POURREZA H, BALOUİ JAMKHANEH E, DEİRİ E, GARG H. Estimating the Parametric Functions and Reliability Measures for Exponentiated Lifetime Distributions Family. GAZI UNIVERSITY JOURNAL OF SCIENCE 2022. [DOI: 10.35378/gujs.910897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
|
2
|
A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model. Symmetry (Basel) 2021. [DOI: 10.3390/sym13071226] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.
Collapse
|
3
|
Al-Kzzaz HS, Abd El-Monsef MME. Inverse power Maxwell distribution: statistical properties, estimation and application. J Appl Stat 2021; 49:2287-2306. [DOI: 10.1080/02664763.2021.1899143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- H. S. Al-Kzzaz
- Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
| | | |
Collapse
|
4
|
Saini S, Chaturvedi A, Garg R. Estimation of stress–strength reliability for generalized Maxwell failure distribution under progressive first failure censoring. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2020.1856846] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Shubham Saini
- Department of Statistics, University of Delhi, Delhi, India
| | | | - Renu Garg
- Department of Statistics, University of Delhi, Delhi, India
| |
Collapse
|
5
|
Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2020. [DOI: 10.3390/mca25040065] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall–Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall–Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills.
Collapse
|
6
|
A Review on Inverse Maxwell Distribution with Its Statistical Properties and Applications. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2020. [DOI: 10.1007/s42519-020-00100-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
7
|
Chaturvedi A, Vyas S. Generalized Gamma - Maxwell distribution: Properties and estimation of reliability functions. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2019. [DOI: 10.1080/09720510.2019.1609553] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Ajit Chaturvedi
- Department of Statistics, University of Delhi, Delhi 110007, India
| | - Shantanu Vyas
- Department of Statistics, Amity Institute of Applied Sciences, Amity University, Noida 201003, India
| |
Collapse
|
8
|
Sindhu TN, Hussain Z, Aslam M. Parameter and reliability estimation of inverted Maxwell mixture model. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2019. [DOI: 10.1080/09720510.2018.1552412] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Tabassum Naz Sindhu
- Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan, E-mails: ,
| | - Zawar Hussain
- Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan, E-mails: ,
| | - Muhammad Aslam
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia
| |
Collapse
|
9
|
Chaudhary S, Kumar J, Tomer SK. Estimation of P[Y < X] for Maxwell distribution. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2017. [DOI: 10.1080/09720510.2017.1308064] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sachin Chaudhary
- Department of Statistics, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
| | - J. Kumar
- Department of Statistics, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
| | - Sanjeev K. Tomer
- Department of Statistics, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
| |
Collapse
|
10
|
Saghir A, Khadim A, Lin Z. The Maxwell length-biased distribution: Properties and estimation. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2016. [DOI: 10.1080/15598608.2016.1246266] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Aamir Saghir
- Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan
| | - Aneeqa Khadim
- Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan
| | - Zhengyan Lin
- Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou, P.R. China
| |
Collapse
|
11
|
|
12
|
MirMostafaee SMTK, Mahdizadeh M, Lemonte AJ. The Marshall–Olkin extended generalized Rayleigh distribution: Properties and applications. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2014.1002937] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
13
|
Dey S, Dey T, Ali S, Mulekar MS. Two-parameter Maxwell distribution: Properties and different methods of estimation. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2016. [DOI: 10.1080/15598608.2015.1135090] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
14
|
Krishna H, Vivekanand, Kumar K. Estimation in Maxwell distribution with randomly censored data. J STAT COMPUT SIM 2014. [DOI: 10.1080/00949655.2014.986483] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
15
|
|
16
|
Tomer SK, Panwar MS. Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme. J STAT COMPUT SIM 2013. [DOI: 10.1080/00949655.2013.822871] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
17
|
Kazmi SMA, Aslam M, Ali S, Abbas N. Selection of suitable prior for the Bayesian mixture of a class of lifetime distributions under type-I censored datasets. J Appl Stat 2013. [DOI: 10.1080/02664763.2013.789831] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
18
|
Gomes AE, da-Silva CQ, Cordeiro GM, Ortega EM. A new lifetime model: the Kumaraswamy generalized Rayleigh distribution. J STAT COMPUT SIM 2012. [DOI: 10.1080/00949655.2012.706813] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
19
|
Krishna H, Malik M. Reliability estimation in Maxwell distribution with progressively Type-II censored data. J STAT COMPUT SIM 2012. [DOI: 10.1080/00949655.2010.550291] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
20
|
Cordeiro GM, Cristino CT, Hashimoto EM, Ortega EMM. The beta generalized Rayleigh distribution with applications to lifetime data. Stat Pap (Berl) 2011. [DOI: 10.1007/s00362-011-0415-0] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
21
|
|
22
|
Cordeiro GM, Ortega EM, Silva GO. The exponentiated generalized gamma distribution with application to lifetime data. J STAT COMPUT SIM 2011. [DOI: 10.1080/00949650903517874] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
23
|
Dey S, Maiti SS. Bayesian Estimation of the Parameter of Maxwell Distribution under Different Loss Functions. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2010. [DOI: 10.1080/15598608.2010.10411986] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
24
|
Krishna H, Malik M. Reliability estimation in Maxwell distribution with Type‐II censored data. INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGEMENT 2009. [DOI: 10.1108/02656710910928815] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|