1d:T7bf,# Get the GLD Parameters from the moments Calculates the parameters of the generalized lambda distribution (FKML), given the first four moments of the distribution. ```r s.gld.from.moments( mean = 0, variance = 1, skewness = 0, excessKurtosis = 0, type = 0, start = NULL, nelderMeadOptions = get.options.neldermead() ) ``` ## Arguments - `mean`: A number for the mean of the distribution. - `variance`: A number for the variance of the distribution. - `skewness`: A number for the skewness of the distribution. - `excessKurtosis`: A number for the excess kurtosis of the distribution. - `type`: An integer to restrict the shape of the distribution. See details section. - `start`: A numeric vector of size 2 for the starting value. - `nelderMeadOptions`: A list of options for Nelder-Mead algorithm. Use get.options.neldermead for initialization. ## Returns A vector of length 5. The first 4 elements are the parameters of the GLD distribution. The last one is the number of iterations. ## Details The type of the distribution is determined by one or two restrictions: * type 0: general, no restriction * type 1: symmetric 'type 0', p3 == p4 * type 2: uni-modal continuous tail, p3 \< 1 & p4 \< 1 * type 3: symmetric 'type 2', p3 == p4 * type 4: uni-modal continuous tail finite slope, p3 \<= 0.5 & p4 \<= 0.5 * type 5: symmetric 'type 4', p3 == p4 * type 6: uni-modal truncated density curves, p3 \>= 2 & p4 \>= 2 (includes uniform distribution) * type 7: symmetric 'type 6', p3 == p4 * type 8: S shaped, (p3 \> 2 & 1 \< p4 \< 2) or (1 \< p3 \< 2 & p4 \> 2) * type 9: U shaped, (1 \< p3 \<= 2) and (1 \< p4 \<= 2) * type 10: symmetric 'type 9', p3 == p4 * type 11: monotone, p3 \> 1 & p4 \<= 1 ## Examples ```r res <- s.gld.from.moments(0,1,0,0, start = c(0,0), type = 4) probs <- seq(0.1,0.9,0.1) x <- s.gld.quantile(probs, res[1],res[2],res[3],res[4]) y <- s.gld.density.quantile(probs, res[1],res[2],res[3],res[4]) plot(x,y) lines(x,y) ```

s.gld.from.moments function