On the characteristic and moment generating functions of type-2 (Fréchet) and type-3 (reversed Weibull) distributions
Author Affiliations
- 1Centre for Marine Technology and Ocean Engineering (Centec), Instituto Superior Técnico, Universidade de Lisboa, Av.Rovisco Pais, 1049-001, Lisbon, Portugal
- 2Centre for Marine Technology and Ocean Engineering (Centec), Instituto Superior Técnico, Universidade de Lisboa, Av.Rovisco Pais, 1049-001, Lisbon, Portugal
Res. J. Mathematical & Statistical Sci., Volume 5, Issue (4), Pages 12-14, April,12 (2017)
Abstract
We are able to derive for the first time the simplest forms of characteristic functions (CHFs) and moment generating functions (MGF)of type-2(Fréchet)and type-3 (reversed Weibull)in explicit closed forms by direct and unique methodology. CHF and MGF have wide applications in statistical theories such as in inversion and convolution.
References
- Jenkinson A.F. (1955)., The Frequency Distribution of the Annual Maximum (or Minimum) Values of Meteorological Elements., Quart. J. Roy. Met. Soc., 81(348), 158-171.
- Jenkinson A.F. (1969)., Estimation of Maximum Floods., World Meteorological Organization, Technical Note, 98, 183-257.
- Natural Environment Research Council (1975)., Flood Studies Report., 1, London.
- Sinclair C.D. and Ahmad M.I. (1988)., Location-Invariant Plotting Positions for PWM Estimation of the parameters of GEV Distribution., J.Hydro., 99(3-4), 271-279.
- Otten A. and Van Monfort M.A.J. (1980)., Maximum-Likelihood Estimation of the generalised-extreme value distribution parameters., J. Hydro., 47(1), 187-192.
- Prescott P. and Walden A.T. (1980)., Maximum Likelihood Estimation of the parameters of the Generalised Extreme-Value Distribution., Biometrika, 67, 723-724.
- Prescott P. and Walden A.T. (1983)., Maximum Likelihood Estimation of the parameters of the three parameter Generalised Extreme-Value Distribution from Censored Samples., J. Stat. Comp. Simul., 16(3-4), 241-250.
- Hosking J.R.M., Wallis J.R. and Wood E.F. (1985)., Estimation of the Generalised Extreme Value Distribution by the Method of Probability-Weighted Moments., Technometrics, 27(3), 251-261.
- Nadarajah S. and Pogány T.K. (2013)., On the Characteristic Functions for Extreme Value Distributions., Extremes, 16, 27-38.
- Muraleedharan G., Guedes C. and Lucas C. (2011)., Characteristic and Moment Generating Functions of Generalised Extreme Value Distribution (GEV). Sea Level Rise, Coastal Engineering, Shorelines and Tides., Chapter-14, Nova Science Publishers, New York, 269-276. (ISBN: 978-1-61728-655-1)
- Maurice George Kendall (1946)., The Advanced Theory of Statistics., Distribution Theory, 1, Charles Griffin and Co. Ltd., London, 433.
- Ochi Michel K. (1998)., Ocean Waves: Ocean Technology Series-6, Cambridge University Press., Cambridge, 319.