×

zbMATH — the first resource for mathematics

The beta generalized half-normal distribution. (English) Zbl 05689645
Summary: For the first time, we propose the so-called beta generalized half-normal distribution, which contains some important distributions as special cases, such as the half-normal and generalized half-normal (Cooray and Ananda, 2008) distributions. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments of the new distribution. We examine the maximum likelihood estimation of the parameters and provide the expected information matrix. The usefulness of the new distribution is illustrated through a real data set by showing that it is quite flexible in analyzing positive data instead of the generalized half-normal, half-normal, Weibull and beta Weibull distributions.

MSC:
62 Statistics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aarset, M.V., How to identify bathtub hazard rate, IEEE transactions reliability, 36, 106-108, (1987) · Zbl 0625.62092
[2] Aarts, R.M., (2000). Lauricella functions. www.mathworld.com/LauricellaFunctions.html. From MathWorld — A Wolfram Web Resouce, created by Eric W. Weisstein
[3] Bebbington, M.; Lai, C.D.; Zitikis, R., A flexible Weibull extension, Reliability engineering and system safety, 92, 719-726, (2007)
[4] Carrasco, J.M.F.; Ortega, E.M.M.; Cordeiro, G.M., A generalized modified Weibull distribution for lifetime modeling, Computational statistics and data analysis, 53, 450-462, (2008) · Zbl 1231.62015
[5] Cooray, K.; Ananda, M.M.A., A generalization of the half-normal distribution wit applications to lifetime data, Communication in statistics — theory and methods, 37, 1323-1337, (2008) · Zbl 1163.62006
[6] Díaz-García, J.A.; Leiva, V., A new family of life distributions based on elliptically contoured distributions, Journal of statistical planning and inference, 137, 1512-1513, (2005)
[7] Doornik, J., Ox: an object-oriented matrix programming language, (2007), International Thomson Business Press
[8] Eugene, N.; Lee, C.; Famoye, F., Beta-normal distribution and its applications, Communication in statistics - theory and methods, 31, 497-512, (2002) · Zbl 1009.62516
[9] Exton, H., Handbook of hypergeometric integrals: theory, applications, tables, computer programs, (1978), Halsted Press New York · Zbl 0377.33001
[10] Feigl, P.; Zelen, M., Estimation of exponential survival probabilities with concomitant information, Biometrics, 21, 826-837, (1965)
[11] Gradshteyn, I.S.; Ryzhik, I.M., Table of integrals, series, and products, (2000), Academic Press San Diego · Zbl 0981.65001
[12] Haupt, E.; Schabe, H., A new model for a lifetime distribution with bathtub shaped failure rate, Microelectronic and reliability, 32, 633-639, (1992)
[13] Hosking, J.R.M., \(L\)-moments: analysis and estimation of distributions using linear combinations of order statistics, Journal of the royal statistical society, series B, 52, 105-124, (1990) · Zbl 0703.62018
[14] Jones, M.C., Families of distribution arising from distribution of order statistics, Test, 13, 1-43, (2004) · Zbl 1110.62012
[15] Lai, C.D.; Xie, M.; Murthy, D.N.P., A modified Weibull distribution, IEEE transactions reliability, 52, 33-37, (2003)
[16] Lee, C.; Famoye, F.; Olumolade, O., Beta-Weibull distribution: some properties and applications to censored data, Journal of modern applied statistical methods, 6, 173-186, (2007)
[17] Mudholkar, G.S; Srivastava, D.K.; Friemer, M., The exponential Weibull family: A reanalysis of the bus-motor failure data, Technometrics, 37, 436-445, (1995) · Zbl 0900.62531
[18] Mudholkar, G.S; Srivastava, D.K.; Friemer, M., A generalization of the Weibull distribution with application to the analysis of survival data, Journal of the American statistical association, 91, 1575-1583, (1996) · Zbl 0881.62017
[19] Nadarajah, S., Explicit expressions for moments of order statistics, Statistics and probability letters, 78, 196-205, (2008) · Zbl 1290.62023
[20] Nadarajah, S.; Gupta, A.K., The beta Fréchet distribution, Far east journal of theorical statistics, 15, 15-24, (2004) · Zbl 1074.62008
[21] Nadarajah, S.; Kotz, S., The beta Gumbel distribution, Mathematical problems in engineering, 10, 323-332, (2004) · Zbl 1068.62012
[22] Nadarajah, S.; Kotz, S., The beta exponential distribution, Reliability engineering and system safety, 91, 689-697, (2005)
[23] Nelson, W.B., Accelerated testing: statistical models, test plans and data analysis, (1990), Wiley New York
[24] Pham, H.; Lai, C.D., On recent generalizations of the Weibull distribution, IEEE transactions on reliability, 56, 454-458, (2007)
[25] Rajarshi, S.; Rajarshi, M.B., Bathtub distributions: A review, Communication in statistics — theory and methods, 17, 2597-2621, (1988) · Zbl 0696.62027
[26] Trott, M., The Mathematica guidebook for symbolics. with 1 DVD-ROOM (windows, macintosh and UNIX), (2006), springer New York
[27] Xie, M.; Lai, C.D., Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function, Reliability engineering and system safety, 52, 87-93, (1995)
[28] Xie, M.; Tang, Y.; Goh, T.N., A modified Weibull extension with bathtub failure rate function, Reliability engineering and system safety, 76, 279-285, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.