Article

# 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: 1.3). 01/2008; 53(2):477-485. DOI: 10.1016/j.csda.2008.08.012 Source: RePEc

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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. 04/2012; 46(2):197-214. - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the structure of inter-industry relationships using networks of money flows between industries in 20 national economies. We find these networks vary around a typical structure characterized by a Weibull link weight distribution, exponential industry size distribution, and a common community structure. The community structure is hierarchical, with the top level of the hierarchy comprising five industry communities: food industries, chemical industries, manufacturing industries, service industries, and extraction industries.Physica A: Statistical Mechanics and its Applications 04/2012; · 1.68 Impact Factor -
##### Article: The beta log-normal distribution

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**ABSTRACT:**For the first time, we introduce the beta log-normal (LN) distribution for which the LN distribution is a special case. Various properties of the new distribution are discussed. Expansions for the cumulative distribution and density functions that do not involve complicated functions are derived. We obtain expressions for its moments and for the moments of order statistics. The estimation of parameters is approached by the method of maximum likelihood, and the expected information matrix is derived. The new model is quite flexible in analysing positive data as an important alternative to the gamma, Weibull, generalized exponential, beta exponential, and Birnbaum–Saunders distributions. The flexibility of the new distribution is illustrated in an application to a real data set.Journal of Statistical Computation and Simulation 07/2011; iFirst(2011). · 0.63 Impact Factor

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