Selection between Weibull and lognormal distributions: A comparative simulation study

How to select the correct distribution for a given set of data is an important issue, especially when the tail probabilities are of interest as in lifetime data analysis. The Weibull and lognormal distributions are assumed most often in analyzing lifetime data, and in many cases, they are competing with each other. In addition, lifetime data are usually censored due to the constraint on the amount of testing time. A literature review reveals that little attention has been paid to the selection problems for the case of censored samples. In this article, relative performances of the two selection procedures, namely, the maximized likelihood and scale invariant procedures are compared for selecting between the Weibull and lognormal distributions for the cases of not only complete but also censored samples. Monte Carlo simulation experiments are conducted for various combinations of the censoring rate and sample size, and the performance of each procedure is evaluated in terms of the probability of correct selection (PCS) and average error rate. Then, previously unknown behaviors and relative performances of the two procedures are summarized. Computational results suggest that the maximized likelihood procedure can be generally recommended for censored as well as complete sample cases.

[1]  Sang Gil Kang,et al.  Bayesian model selection for life time data under type II censoring , 2000 .

[2]  Satish K. Agarwal,et al.  Extended Weibull type distribution and finite mixture of distributions , 2006 .

[3]  Debasis Kundu,et al.  Discriminating between Weibull and generalized exponential distributions , 2003, Comput. Stat. Data Anal..

[4]  I. Olkin,et al.  Can data recognize its parent distribution , 1999 .

[5]  Md. Borhan Uddin,et al.  Selection of probability distribution for life testing data , 1991 .

[6]  Min Xie,et al.  Failure Data Analysis with Extended Weibull Distribution , 2007, Commun. Stat. Simul. Comput..

[7]  R. F. Kappenman,et al.  A simple method for choosing between the lognormal and weibull models , 1988 .

[8]  Vijay P. Singh,et al.  Probability of correct selection from lognormal and convective diffusion models based on the likelihood ratio , 2006 .

[9]  D. N. Prabhakar Murthy,et al.  Weibull model selection for reliability modelling , 2004, Reliab. Eng. Syst. Saf..

[10]  R. F. Kappenman,et al.  On A method for selecting a distributional model , 1982 .

[11]  D. Kundu,et al.  Discriminating between gamma and generalized exponential distributions , 2004 .

[12]  Michael R Flynn,et al.  The 4-parameter lognormal (SB) model of human exposure. , 2004, The Annals of occupational hygiene.

[13]  Siswadi,et al.  Selecting among weibull, lognormal and gamma distributions using complete and censored smaples , 1982 .

[14]  Colin Chen.  Tests of fit for the three-parameter lognormal distribution , 2006, Comput. Stat. Data Anal..

[15]  Lawrence Leemis,et al.  Parametric Model Discrimination for Heavily Censored Survival Data , 2008, IEEE Transactions on Reliability.

[16]  M. A. Ismail,et al.  Mixture of two inverse Weibull distributions: Properties and estimation , 2007, Comput. Stat. Data Anal..

[17]  V. Singh,et al.  Three procedures for selection of annual flood peak distribution , 2006 .

[18]  M. Lee,et al.  Model selection for the rate problem: A comparison of significance testing, Bayesian, and minimum description length statistical inference , 2006 .

[19]  F. Downton,et al.  Statistical analysis of reliability and life-testing models : theory and methods , 1992 .

[20]  P. Sen,et al.  Theory of rank tests , 1969 .

[21]  A. Louisa,et al.  コロイド混合体における有効力 空乏引力から集積斥力へ | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 2002 .

[22]  E. J. Dick,et al.  Beyond ‘lognormal versus gamma’: discrimination among error distributions for generalized linear models , 2004 .

[23]  Wayne Nelson,et al.  Applied life data analysis , 1983 .

[24]  José A. Díaz-García,et al.  A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation , 2008, Computational Statistics & Data Analysis.

[25]  J Bain Lee,et al.  Probability of correct selection of weibull versus gamma based on livelihood ratio , 1980 .

[26]  C. Quesenberry,et al.  Selecting Among Probability Distributions Used in Reliability , 1982 .

[27]  Richard M. Bennett,et al.  Three-parameter vs. two-parameter Weibull distribution for pultruded composite material properties , 2002 .

[28]  Debasis Kundu,et al.  Discriminating between the generalized Rayleigh and Log-normal distribution , 2007 .

[29]  James R. Lloyd,et al.  On the log‐normal distribution of electromigration lifetimes , 1979 .

[30]  Chiou-Feng Chen,et al.  The dielectric reliability of intrinsic thin SiO 2 films thermally grown on a heavily doped Si substrate—characterization and modeling , 1987 .

[31]  Debasis Kundu,et al.  Discriminating between the Weibull and log‐normal distributions , 2004 .

[32]  M. Peshwani,et al.  Choice Between Weibull and Lognormal Models: A Simulation Based Bayesian Study , 2003 .

[33]  Hoang Pham,et al.  On Recent Generalizations of the Weibull Distribution , 2007, IEEE Transactions on Reliability.

[34]  Franz Dieter Fischer,et al.  Fracture statistics of brittle materials: Weibull or normal distribution. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Michael R. Flynn.  On the Moments of the 4-Parameter Lognormal Distribution , 2005 .

[36]  Mario Pinto.  The effect of Barrier layers on the distribution function of interconnect electromigration failures , 1991 .

[37]  Basilio de Bragança Pereira,et al.  A Comparison of Bayes Factors for Separated Models: Some Simulation Results , 2003, Commun. Stat. Simul. Comput..

[38]  D. Kundu,et al.  Discriminating between the log-normal and generalized exponential distributions , 2005 .

[39]  Geert Molenberghs,et al.  The time of “guessing” your failure time distribution is over! , 1998 .

[40]  Stephen R. Cain,et al.  Distinguishing between lognormal and Weibull distributions [time-to-failure data] , 2002, IEEE Trans. Reliab..

[41]  James Prendergast,et al.  Investigation into the correct statistical distribution for oxide breakdown over oxide thickness range , 2005, Microelectron. Reliab..

[42]  Debasis Kundu,et al.  Is Weibull distribution the most appropriate statistical strength distribution for brittle materials , 2009 .