This work introduces three different approximations to the distribution of weighted log-normal variates. Numerical methods are used to express the density function as a Gauss-Hermite quadrature and a Gauss-Laguerre quadrature. The third approximation was the expression of the density function as a mixture of gamma function. Numerical examples are given to demonstrate the method and equality of the first four moments are observed. However, a general method is introduced to equate as many moments as required.
El Mawaziny, A., & Rashad, H. (1976). Approximations to the Distribution of Weighted Log-Normal Variates. The Egyptian Statistical Journal, 20(1), 38-57. doi: 10.21608/esju.1976.315750
MLA
Ahmed H. El Mawaziny; Hoda M. Rashad. "Approximations to the Distribution of Weighted Log-Normal Variates", The Egyptian Statistical Journal, 20, 1, 1976, 38-57. doi: 10.21608/esju.1976.315750
HARVARD
El Mawaziny, A., Rashad, H. (1976). 'Approximations to the Distribution of Weighted Log-Normal Variates', The Egyptian Statistical Journal, 20(1), pp. 38-57. doi: 10.21608/esju.1976.315750
VANCOUVER
El Mawaziny, A., Rashad, H. Approximations to the Distribution of Weighted Log-Normal Variates. The Egyptian Statistical Journal, 1976; 20(1): 38-57. doi: 10.21608/esju.1976.315750
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