Browse > Article
http://dx.doi.org/10.5351/CSAM.2017.24.1.015

A two-parameter discrete distribution with a bathtub hazard shape  

Sarhan, Ammar M. (Department of Mathematics and Statistics, Dalhousie University)
Publication Information
Communications for Statistical Applications and Methods / v.24, no.1, 2017 , pp. 15-27 More about this Journal
Abstract
This paper introduces a two-parameter discrete distribution based on a continuous two-parameter bathtub distribution. It is the only two-parameter discrete distribution that shows a bathtub-shaped hazard function. Some statistical properties of the distribution are discussed. Three different methods are used to estimate its two unknown parameters. The point estimators of the parameters have no closed form. The bootstrap method is used to estimate the distributions of these point estimators. Different approximations of the interval estimations for the two-parameters are discussed. Real data sets are analyzed to show how this distribution works in practice. A simulation study is performed to investigate the properties of the estimations obtained and compare their performances.
Keywords
maximum likelihood estimator; likelihood interval; least square; quartile; reliability; lifetime models;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Chen Z (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, 49, 155-161.   DOI
2 Gnedenko BV and Ushakov IA (1995). Probabilistic Reliability Engineering, John Wiley & Sons, New York.
3 Kalbfleisch JG (1985). Probability and Statistical Inference (Volume 2: Statistical Inference), Springer -Verlag, New York.
4 Kapur KC and Lamberson LR (1977). Reliability and Engineering Design, John Wiley & Sons, New York.
5 Lai CD, Xie M, and Murthy DNP (2003). A modified Weibull distribution, IEEE Transactions on Reliability, 25, 33-37.
6 Lawless JF (1982). Statistical Models and Methods for Lifetime Data, JohnWiley & Sons, New York.
7 Nakagawa T and Osaki S (1975). The discreteWeibull distribution, IEEE Transactions on Reliability, R-24, 300-301.   DOI
8 Nooghabi MS, Borzadaran GRM, and Roknabadi AHR (2012). Discrete modified Weibull distribution, Metron, 69, 207-222.
9 Padgett WJ and Spurrier JD (1985). On discrete failure models, IEEE Transactions on Reliability, 34, 253-256.
10 Roy D (2003). The discrete normal distribution, Communications in Statistics - Theory and Methods, 32, 1871-1883.   DOI
11 Roy D (2004). Discrete Rayleigh distribution, IEEE Transactions on Reliability, 53, 255-260.   DOI
12 Schwarz G (1978). Estimating the dimension of a model, Annals of Statistics, 6, 461-464.   DOI
13 Sinha SK (1986). Reliability and Life Testing, John Wiley & Sons, New York.
14 Stein WE and Dattero R (1984). A new discrete Weibull distribution, IEEE Transactions on Reliability, 33, 196-197.
15 Wang FK (2000). A new model with bathtub-shaped failure rate using an additive Burr XII distribution, Reliability Engineering and System Safety, 70, 305-312.   DOI
16 Aarset MV (1987). How to identify a bathtub hazard rate, IEEE Transactions on Reliability, R-36, 106-108.   DOI
17 Almalki SJ (2013). A reduced new modified Weibull distribution, Retrieved January 17, 2017, from: http://arxiv.org/abs/1307.3925
18 Al-Huniti AA and Al-Dayian GR (2012). Discrete Burr type III distribution, American Journal of Mathematics and Statistics, 2, 145-152.   DOI
19 Wasserman L (2006). All of Nonparametric Statistics, Springer, New York.
20 Xie M and Lai CD (1996). Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function, Reliability Engineering and System Safety, 52, 87-93.   DOI
21 Almalki SJ and Nadarajah S (2014). A new discrete modifiedWeibull distribution, IEEE Transactions on Reliability, 63, 68-80.   DOI
22 Bebbington M, Lai CD, Wellington M, and Zitikis R (2012). The discrete additive Weibull distribution: a bathtub-shaped hazard for discontinuous failure data, Reliability Engineering and System Safety, 106, 37-44.   DOI