Abstract
In this article, we consider a lifetime distribution, the Weibull-Logarithmic distribution introduced by [6]. We investigate some new statistical characterizations and properties. We develop the maximum likelihood inference using EM algorithm. Asymptotic properties of the MLEs are obtained and extensive simulations are conducted to assess the performance of parameter estimation. A numerical example is used to illustrate the application.
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References
K Adamidis, S Loukas. A lifetime distribution with decreasing failure rate, Statist Probab Lett, 1998, 39(1): 35–42.
B Arnold, N Balakrishnan, H Nagaraja. A First Course in Order Statistics, Classics in Applied Mathematics, vol 54, SIAM, 1992.
R Barlow, R Toland, T Freeman. A Bayesian analysis of the stress-rupture life of kevlar/epoxy spherical pressure vessels, In: Accelerated Life Testing and Experts’ Opinions in Reliability, C A Clarotti, D V Lindley, eds, 1988.
W Barreto-Souza, A L de Morais, G M Cordeiro. The Weibull-geometric distribution, J Stat Comput Simul, 2011, 81(5): 645–657.
L Castro, H Gómez, M Valenzuela. Epsilon half-normal model: properties and inference, Comput Statist Data Anal, 2012.
R Ciumara, V Preda. The Weibull-logarithmic distribution in lifetime analysis and its properties, In: The XIII International Conference Applied Stochastic Models and Data Analysis, L Sakalauskas, C Skiadas, and E K Zavadskas, eds, 2009, pp395–399.
D Cox, D Hinkley. Theoretical Statistics, Chapman & Hall/CRC, 1979.
A P Dempster, N M Laird, D B Rubin. Maximum likelihood from incomplete data via the EM algorithm, J R Stat Soc Ser B Methodol, 1977, 39(1): 1–38.
D L Evans, J H Drew, L M Leemis. The distribution of the Kolmogorov–Smirnov, Cramer–Von mises, and Anderson–Darling test statistics for Exponential populations with estimated parameters, Comm Statist Simulation Comput, 2008, 37(7): 1396–1421.
W Gui, P-H Chen, H Wu. An epsilon half normal slash distribution and its applications to nonnegative measurements, Open J Optim, 2013, 2(1): 1–8.
N L Johnson, A W Kemp, S Kotz. Univariate Discrete Distributions, Vol 444, John Wiley & Sons, 2005.
N Olmos, H Varela, H Gómez, H Bolfarine. An extension of the half-normal distribution, Statist Papers, 2012, 53(4): 875–886.
C Ramesh, S Kirmani. On order relations between reliability measures, Stoch Models, 1987, 3(1): 149–156.
R Tahmasbi, S Rezaei. A two-parameter lifetime distribution with decreasing failure rate, Comput Statist Data Anal, 2008, 52(8): 3889–3901.
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Supported by the program for the Fundamental Research Funds for the Central Universities (2014RC042, 2015JBM109).
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Gui, Wh., Zhang, Hn. Asymptotic properties and expectation-maximization algorithm for maximum likelihood estimates of the parameters from Weibull-Logarithmic model. Appl. Math. J. Chin. Univ. 31, 425–438 (2016). https://doi.org/10.1007/s11766-016-3391-2
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DOI: https://doi.org/10.1007/s11766-016-3391-2