Univariate Weibull Distributions and Their Applications
Ključne riječi:
univariate Weibull distribution, multivariate Weibull distribution, application areas, p.d.f, c.d.f, maximum likelihood estimationSažetak
The aim of the paper is to bring out the short and concise review of the Univariate Weibull distributions along with their properties. The area of applications is emphasized at the end of the sections.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Reference
Azzalini, A. (2005), “The Skew - normal Distribution and Related Multivariate Families”, Board of the Foundation of the Scandinavian Journal of Statistics, Vol. 32, pp. 159-188.
Ayebo, A., Kozubowski, T.J. (2003), “An asymmetric generalization of Gaussian and Laplace laws”, Journal of Probability and Statistical Science, Vol. 1 No. 2, pp. 187-210.
Balakrishnan N., Kocherlakota, S. (1985), “On the double Weibull distribution: Order statisticsand estimation”, Indian Journal of Statistics, Vol. 47, pp. 161-178.
Berrettoni, J.N. (1964), “Practical applications of the Weibull distribution”, Industrial Quality Control, Vol. 21, pp. 71-79.
Boothe, P., Glassman, D. (1987), “The statistical distribution of exchange rates”, Journal of International Economics, Vol. 22, pp. 297-319.
Chenyao, D., Mittnik, S., Rachev, S.T. (1996), “Distribution of exchange rates: a geometric summation-stable model”, Proceedings of the Seminar on Data Analysis, Sept. 12-17, Sozopol, Bulgaria.
Cohen, A.C. (1965), “Maximum likelihood estimation in the Weibull distribution based on complete and on censored samples”, Technometrics, Vol. 7, pp. 579-588.
Dattatreya Rao, A.V., Narasimham, V.L. (1989), “Linear estimation in double Weibull distribution, “Indian Journal of Statistics”, Vol. 51, pp. 24-64.
Fernandez, C., Steel, M.F.J. (1998), “On Bayesian modeling of fat tails and skewness”, Journal of the American Statistical Association, Vol. 93, pp. 359-371.
Harter, H.L., Moore, A.H. (1968), “Maximum likelihood estimation from doubly censored samples of the parameters of the first asymptotic
Koedijk, K.G., Schafgans, M.M., de Vries, C.G. (1990), “The tail index of exchange rates returns”, Journal of International Economics, Vol. 29, pp. 93-108.
Kotz, S., Kozubowski, T.J., Podgo´rski, K. (2001), The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance, Birkh¨auser, Boston.
Kozubowski, T.J., Podgo´rski, K. (2000), “Asymmetric Laplace distributions”, The Mathematical Scientist, Vol. 25, pp. 37-46.
Kozubowski, T.J., Podgo´rski, K. (2001), “Asymmetric Laplace laws and modeling financial data”, Mathematical and Computer Modelling, Vol. 34, pp. 1003-1021.
McCool, J.I. (1970), “Inferences on Weibull percentiles and shape parameter from maximum likelihood estimates”, IEEE Transactions on Reliability, R-19, pp. 2-9.
McFarland, J.W., Pettit, R.R., Sung, S.K. (1982), “The distribution of foreign exchange pricechanges: Trading day effects and risk measurement”, Journal of Finance, Vol. 37 No. 3, pp. 693-715.
Mittnik, S., Rachev S.T. (1993), “Modeling asset returns with alternative stable distributions”, Econometric Reviews, Vol. 12 No. 3, pp. 261-330.
Nolan, J.P. (2001), “Maximum likelihood estimation and diagnostic for stable distributions”, In: L´evy processes: Theory and Applications (Barndorff-Nielsen et al., eds.), Birkha¨user, Boston, pp. 379-400.
Pike, M. (1966), “A suggested method of analysis of a certain class of experiments in carcinogenesis”, Biometrics, Vol. 22, pp. 142-161.
Rockette, H., Antle, C., Klimko, L.A. (1974), “Maximum likelihood estimation with the Weibull model”, Amer. Statist. Assoc., Vol. 69.
Tucker, A.L., Pond, L. (1988), ”Probability distribution of exchange rate changes”, Review of Economical Studies, Vol. 70, pp. 638-647.
Westerfield, J.M. (1977), “An examination of foreign exchange risk under fixed and floating rate regimes”, Journal of International Economics, Vol. 7, pp. 181-200.
