The beta log-normal distribution

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...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2013-02, Vol.83 (2), p.203-228
Main Authors: Castellares, F., Montenegro, L. C., Cordeiro, G. M.
Format: Article
Language:English
Subjects:
Beta
Beta log-normal distribution
Bonferroni curve
Computation
Computer simulation
Density
Distribution
entropy
Flexibility
log-normal distribution
Lorentz curve
Mathematical analysis
Mathematical models
Matrix
Maximum likelihood method
maximum-likelihood estimation
moment
observed information matrix
order statistic
Parameter estimation
Statistics
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Summary: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.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2011.599809