%0 Journal Article %1 kotz64 %A Kotz, Samuel %A Adams, John W. %D 1964 %J The Annals of Mathematical Statistics %K correlates distribution exponential gamma imported limit mathematics probability sum %N 1 %P 277-283 %T Distribution of Sum of Identically Distributed Exponentially Correlated Gamma-Variables %U http://links.jstor.org/sici?sici=0003-4851%28196403%2935%3A1%3C277%3ADOSOID%3E2.0.CO%3B2-C %V 35 %X A distribution of a sum of identically distributed Gamma- variables correlated according to an "exponential" autocorrelation law pkj = p'k-jl(k, j = 1, . . . n) where pkj is the correlation coefficient between the kth and jth random variables and 0 < p < 1 is a given number is derived. An äpproximate" distribution of the sum of these variables under the assumption that the sum itself is a Gamma-variable is given. A comparison between exact and approximate distributions for certain values of the 'correlation coefficient, the number of variables in the sum and the values of parameters of the initial dis- tributions is presented.

@article{kotz64, abstract = {A distribution of a sum of identically distributed Gamma- variables correlated according to an "exponential" autocorrelation law pkj = p'k-jl(k, j = 1, . . . n) where pkj is the correlation coefficient between the kth and jth random variables and 0 < p < 1 is a given number is derived. An "approximate" distribution of the sum of these variables under the assumption that the sum itself is a Gamma-variable is given. A comparison between exact and approximate distributions for certain values of the 'correlation coefficient, the number of variables in the sum and the values of parameters of the initial dis- tributions is presented. }, added-at = {2007-10-10T19:43:03.000+0200}, author = {Kotz, Samuel and Adams, John W.}, biburl = {https://www.bibsonomy.org/bibtex/2e35039a3b699b85e0c7470143da6558e/andreab}, description = {JSTOR: Annals of Mathematical Statistics: Vol. 35, No. 1, pp. 277-283}, interhash = {b4be85354761b4886627d423abcca49a}, intrahash = {e35039a3b699b85e0c7470143da6558e}, journal = {The Annals of Mathematical Statistics}, keywords = {correlates distribution exponential gamma imported limit mathematics probability sum}, month = {March}, number = 1, pages = {277-283}, timestamp = {2007-10-10T19:43:03.000+0200}, title = {Distribution of Sum of Identically Distributed Exponentially Correlated Gamma-Variables }, url = {http://links.jstor.org/sici?sici=0003-4851%28196403%2935%3A1%3C277%3ADOSOID%3E2.0.CO%3B2-C}, volume = {35 }, year = 1964 }