Selection between Weibull and lognormal distributions: A comparative simulation study

Department of Industrial Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-Dong, Yuseong-Gu, Daejeon, 305-701, Republic of Korea
Computational Statistics & Data Analysis (Impact Factor: 1.4). 12/2008; 53(2):477-485. DOI: 10.1016/j.csda.2008.08.012
Source: RePEc


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.

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    • "The use of the lognormal distribution in reliability engineering is quite widespread. For the applications of the lognormal distribution, see Goldthwaite (1961), Mann et al. (1974), Martz and Waller (1982), Crow and Shimizu (1988), and Kim and Yum (2008). Therefore, in this section, we assume that the distribution of the component lifetimes is lognormal. "
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    ABSTRACT: This article considers a system of multiple components connected in parallel. As components fail one by one, the remaining working components share the total load applied to the system. This is commonly referred to as load sharing in the reliability engineering literature. This article considers the traditional approach to the modeling of a load-sharing system under the assumption of the existence of underlying hypothetical latent random variables. Using the Expectation–Maximization (EM) algorithm, a methodology is proposed to obtain the maximum likelihood estimates in such a model in the case where the underlying lifetime distribution of the components is lognormal or normal. The proposed EM method is also illustrated and substantiated using numerical examples. The estimates obtained using the EM algorithm are compared with those obtained using the Broyden–Fletcher–Goldfarb–Shanno algorithm, which falls under the class of numerical methods known as Newton or quasi-Newton methods. The results show that the estimates obtained using the proposed EM method always converge to a unique global maximizer, whereas the estimates obtained using the Newton-type method are highly sensitive to the choice of starting values and thus often fail to converge.
    IIE Transactions 02/2013; 45(2):147-163. DOI:10.1080/0740817X.2012.669878 · 1.37 Impact Factor
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    • ", Kim and Yum [15] and the references cited therein. "
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    ABSTRACT: Log-normal and Weibull distributions are the two most popular distributions for analysing lifetime data. In this paper, we consider the problem of discriminating between the two distribution functions. It is assumed that the data are coming either from log-normal or Weibull distributions and that they are Type-II censored. We use the difference of the maximized log-likelihood functions, in discriminating between the two distribution functions. We obtain the asymptotic distribution of the discrimination statistic. It is used to determine the probability of correct selection in this discrimination process. We perform some simulation studies to observe how the asymptotic results work for different sample sizes and for different censoring proportions. It is observed that the asymptotic results work quite well even for small sizes if the censoring proportions are not very low. We further suggest a modified discrimination procedure. Two real data sets are analysed for illustrative purposes.
    Statistics: A Journal of Theoretical and Applied Statistics 04/2012; 46(2-2):197-214. DOI:10.1080/02331888.2010.504990 · 0.53 Impact Factor
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    • "the parameters thereof being as above. The shape of EMG compared with the generally used distributions is illustrated in Fig. 1, The similarity of all positively skewed curves shown increases upon decreasing their skewness making the choice between them not a trivial matter (see Kim and Yum, 2008). Indeed, any single goodness-of-fit parameter may appear virtually the same for a set of such functions (see Table 1). "
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    ABSTRACT: Positively skewed distributions common in biology are often approximated with lognormal or gamma functions. It is shown here that for some classes of phenomena, including intermitotic time and protein expression variabilities, exponentially modified Gaussian (EMG) may provide better fit. EMG is generated by processes involving normally distributed entry rates and exponentially distributed exit rates; therefore, its parameters may be straightforwardly interpreted in biologically meaningful terms and thus may help to choose between theoretical models of the respective phenomena. In particular, EMG is consistent with the transition probability model of cell cycle and may be used to estimate its deterministic and probabilistic parts. EMG is also consistent with the assumption that the probabilistic part is determined by competing stochastic transcriptional events committing cells to proliferative mitoses, differentiation, or apoptosis. Discrete event simulation modelling of this situation suggests that cell differentiation rate is primarily increased by decreasing the frequencies of the events that result in the realisation of the competing options, including proliferation, rather than by the direct changes in the differentiation-inducing events.
    Journal of Theoretical Biology 01/2010; 262(2-262):257-266. DOI:10.1016/j.jtbi.2009.10.005 · 2.12 Impact Factor
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