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ON LOG-LOGISTIC AND A FOUR-PARAMETER GENERALIZED LOG-LOGISTIC DISTRIBUTIONS

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In this paper, we obtained the distribution of some functions of log-logistic random variables and derived a probability density function that generalizes the distribution. The cumulative distribution function, the nth moment, the me-dian, the mode and the 100k-percentage points of the new generalized distribu-tion are established. Two theorems that relate the new generalized distribution to other statistical distributions are stated and proved.

Abstract

In this paper, we obtained the distribution of some functions of log-logistic random variables and derived a probability density function that generalizes the distribution. The cumulative distribution function, the nth moment, the me-dian, the mode and the 100k-percentage points of the new generalized distribu-tion are established. Two theorems that relate the new generalized distribution to other statistical distributions are stated and proved.

참고문헌 (8)

  1. M.M. Ali, "On order statistics from the log-logistic distribution", Journal of Statistical Planning and Inference, 17, pp.103~108 (1987)
  2. N. Balakrishnan, "Moments of order statistics from truncated log-logistic distribution", Journal of Statistical Planning and Inference, 17, pp.251~267 (1987)
  3. N. Balakrishnan, "Best linear unbiased estimation of location and scale parameters of the log-logistic distribution", Commn. Statist. - theory meth., 16(12), pp.3477~3495 (1987)
  4. I.W. Burr, "Cumulative frequency functions", Ann. Math. Statist., 13, pp.215~232 (1942)
  5. I.W. Burr, "On a general system of distributions III. The sample range", Journal of the American Statistical Association, 62, pp.627~635 (1968)
  6. H.J. Malik, "Exact distribution of the quotient of independent generalized gamma variables", Canadian Mathematical Bulletin, 10, pp.463~466 (1967)
  7. M.O. Ojo, "The distributions of some functions of gamma random variables", Journal of the Nigeria Mathematical Society, 20, pp.91~94 (2001)
  8. K.P. Singh, "A. Warsono, A. Bartoluci and Sejong Bae, Mathematical Modeling of Environmental Data", Mathematical and Computer Modeling, 33, pp.793~800 (2001)

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