TL- MOMENTS AND L-MOMENTS ESTIMATION FOR THE TRANSMUTED WEIBULL DISTRIBUTION
Keywords:
Transmuted Weibull Distribution, Order Statistics, L-moments, TL-moments, Monte Carlo simulationAbstract
Accurate estimation of parameters of a probability distribution is of massive importance in statistics. Biased and vague estimation of parameters can lead to misleading results. The Transmuted Weibull Distribution (TWD) has the advantage of bring capable of modeling various types of data, so the accurate estimation of the parameters of this distribution is required. The main purpose of this paper is to develop the Trimmed Linear moments (TLmoments) of the TWD and use the TL-moments to estimate unknown parameters of the TWD. An special case, linear moments (L-moments) will be obtained and used to estimate the unknown parameters of the TWD. Monte Carlo Simulation technique is used to compare the L-moments and TL-moments of TWD.
Downloads
References
Abdul-Moniem, I. B. (2007). L-moments and TL-moments estimation for the
exponential distribution, Far East J. Theo. Stat., 23(1) p. 51-61.
Abdul-Moniem, I. B. (2009). TL-moments and L-moments estimation for the
Weibull distribution, Advances and Applications in Statistics, 15(1), p. 83-99.
Abdul-Moniem, I. B. and Selim, Y. M. (2009). TL-moments and L-moments
estimation for the generalized Pareto distribution, Applied Mathematical
Sciences, 3(1), p. 43-52.
Aryal, G. R. and Tsokos, C. P. (2011). Transmuted Weibull distribution: a
generalization of the Weibull probability distribution, European Journal of
Pure and Applied Mathematics, 4(2), p. 89-102.
Bilkova, D. (2014). Alternative means of statistical data analysis: L-moments
and TL-moments of probability distributions, Statistika, 94(2), p. 77-94.
Elamir, E. A., Seheult, A. H. (2003). Trimmed L-moments, Computational
Statistics & Data Analysis, 43, p. 299-314.
Hosking, J. (1990). L-moments: Analysis and estimation of distributions using
linear combinations of order statistics, Journal of Royal Statistical Society, B
(1), p. 105-124.
Kundu, D. and Raqab, M. Z. (2005). Generalized Pareto distribution: different
methods of estimations, Computational Statistics & Data Analysis, 49, p. 187-
R Core Team (2015). R: A language and environment for statistical
computing, R Foundation for Statistical Computing, Vienna, Austria. URL
Shaw, W. and Buckley, I. (2007). The alchemy of probability distributions:
beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution
from a rank transmuted map, Research report.
Shazad, N. M., Asghar, S., F. and Shazadi, M. (2015). Parameter estimation of
power function distribution with TL-moments, Revista Colombiana de
Estadistica, 38(2), p. 321-334.
Tomer, S. and Kumar, A. (2014). Traditional moments and L-moments
estimation for the transmuted Exponentiated Lomax distribution,
Anushandhan Anveshika, 4, p. 119-128.
Vogel, R. M. and Fennessey, N. M. (1993). L-moments diagrams should
replace product moments diagrams, Water Resources Research, 29, p. 1745-
