Best linear unbiased estimation of location and scale parameters of the log-logistic distribution

On derive plusieurs relations de recurrence satisfaites par les moments produits des statistiques d'ordre. On montre qu'en commencant avec les k premiers moments existants de la distribution log-logistique on peut evaluer les k premiers moments simples et les moments produits des statistiques d'ordre pour toutes les tailles d'echantillons

[1]  Some general identities involving order statistics , 1985 .

[2]  J O'Quigley,et al.  Survival models based upon the logistic and log--logistic distributions. , 1982, Computer programs in biomedicine.

[3]  H. J. Malik,et al.  Exact Distribution of the Quotient of Independent Generalized Gamma Variables , 1967, Canadian Mathematical Bulletin.

[4]  S. Bennett,et al.  Log‐Logistic Regression Models for Survival Data , 1983 .

[5]  N. Balakrishnan,et al.  A Note on Moments of Order Statistics , 1986 .

[6]  Pranab Kumar Sen,et al.  On the Moments of the Sample Quantiles , 1959 .

[7]  M. J. R. Healy,et al.  Algorithm as 6: Triangular Decomposition of a Symmetric Matrix , 1968 .

[8]  M. J. R. Healy,et al.  Algorithm as 7: Inversion of a Positive Semi‐Definite Symmetric Matrix , 1968 .

[9]  Two identities involving order statistics , 1973 .

[10]  Irving W. Burr,et al.  On A General System of Distributions III. The Sample Range , 1968 .

[11]  J. Green,et al.  On order statistics from thelog-logistic distribution and their properties , 1984 .

[12]  I. W. Burr Cumulative Frequency Functions , 1942 .

[13]  Best linear unbiased estimators of location and scale parameters of the half logistic distribution , 1986 .

[14]  Z. Govindarajulu On Moments of Order Statistics and Quasi-ranges from Normal Populations , 1963 .

[15]  Irving W. Burr,et al.  On A General System of Distributions I. Its Curve-Shape Characteristics II. The Sample Median , 1968 .

[16]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[17]  Pandu R. Tadikamalla,et al.  Systems of frequency curves generated by transformations of logistic variables , 1982 .

[18]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[19]  N. Balakrishnan Order statistics from the half logistic distribution , 1985 .