×

Moment properties of transmuted power function distribution based on order statistics. (English) Zbl 1454.62140

Summary: In this paper, we have obtained the exact expressions for the single and product moments in conjunction with some recurrence relations from transmuted power function (TPF) distribution based on order statistics. We have also obtained the expressions for \(L\)-moments. Further, we compute the first four moments and other statistical properties for the TPF distribution numerically.

MSC:

62G30 Order statistics; empirical distribution functions
62H20 Measures of association (correlation, canonical correlation, etc.)

Software:

LMOMENTS
PDFBibTeX XMLCite
Full Text: Link

References:

[1] Arnold BC, Balakrishnan N, Nagaraja HN. A first course in order statistics. New York: John Wiley; 1992. · Zbl 0850.62008
[2] Balakrishnan N, Cohen AC. Order statistics and inference: estimation methods. San Diego: Academic Press; 1991. · Zbl 0732.62044
[3] Balakrishnan N, Aggarwala R. Relationships for moments of order statistics from the righttruncated generalized half logistic distribution. Ann Inst Stat Math. 1996; 48(3): 519-534. · Zbl 0885.62060
[4] Haq MA, Butt NS, Usman RM, Fattah AA. Transmuted power function distribution. Gazi Univ J Sci. 2016; 29(1): 177-185.
[5] Çetinkaya Ç, Genç Aİ. Moments of order statistics of the standard two-sided power distribution. Commun Stat - Theory Methods. 2018; 47(17): 4311-4328. · Zbl 1508.62130
[6] David HA, Nagaraja HN. Order statistics, New Jersey: John Wiley; 2003. · Zbl 1053.62060
[7] GençAİ. Moments of order statistics of Topp-Leone distribution. Statist Papers. 2012; 53(1): 117-131. · Zbl 1241.62077
[8] Hosking JR. L-moments: analysis and estimation of distributions using linear combinations of order statistics. J Roy Stat Soc B Method. 1990; 52(1): 105-124. · Zbl 0703.62018
[9] Jodrá P. On order statistics from the Gompertz-Makeham distribution and the Lambert W function. Math Model Anal. 2013; 18(3): 432-445. · Zbl 1276.33004
[10] Joshi PC, Balakrishnan N. Recurrence relations and identities for the product moments of order statistics. Sankhya Ser B. 1982; 44(1): 39-49. · Zbl 0534.62028
[11] Khan AH, Yaqub M, Parvez S. Recurrence relations between moments of order statistics. J Stat Plan Infer. 1983; 8(2): 175-183. · Zbl 0524.62048
[12] Kumar D, Dey S. Power generalized Weibull distribution based on order statistics. J Stat Res. 2017; 51(1): 61-78.
[13] Kumar D, Dey S, Nadarajah S. Extended exponential distribution based on order statistics. Commun Stat - Theory Methods. 2017; 46(18): 9166-9184. · Zbl 1377.62135
[14] Malik HJ. Exact moments of order statistics from the Pareto distribution. Scand Actuar J. 1966; (3-4): 144-157. · Zbl 0158.18307
[15] Malik HJ. Exact moments of order statistics from a power-function distribution. Scand Actuar J. 1967; (1-2): 64-69.
[16] Nagaraja HN. Moments of order statistics and L-moments for the symmetrical triangular distribution. Stat Prob Lett. 2013; 83(10): 2357-2363. · Zbl 1285.60011
[17] Saran J, Kumar D, Pushkarna N, Tiwari R. L-moments, TL-moments estimation and recurrence relations for moments of order statistics from exponentiated inverted Weibull distribution. Stat Res Lett.2014; 3: 63-71.
[18] Shaw WT, Buckley IR. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv:0901.0434. 2009.
[19] Abdul Nasir Khan et al. 469 j   uk4 (1) (1v)(1) j
[20] on expanding (A3), we obtain 2j11j1B1j,15j12j1B2j,1
[21] further simplification.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.