On fractional moments of random variables

A study was conducted to find asymptotic expressions for fractional moments of random variables. An approach was suggested that yielded asymptotic formulas for fractional moments of random variables with smaller remainders for a wider range of parameter values as compared with the results of a number of equations. Two cases that were considered in a theorem to demonstrate the asymptotic expressions for fractional moments of random variables included a limiting normal distribution and a limiting exponential distribution. It was found that expanding the integrands in powers of x and using asymptotic expressions for even moments gave the desired result.