Distribution of mean of correlation coefficients

In this paper,we derive a distribution of the mean of k-independent sample correlation coefficients each of which is based on ''n'' pairs of observations. this distribution has been developed by expanding the rth power of the modified bessel function by using the taylor series. the mean distribution of sample correlation coefficients (r) has many applications in the field of medicine,accounting,stock exchange market,economics and finance. particularly,if one is interested to find the distribution of average rate of return correlated with risk free,one may have high and/or low risk,in a multiple investment portfolios. © 2011 pakistan journal of statistics.