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I am trying to plot moments ratio plot with the following code:

f1[al_, be_, ga_, lam_] = 
  Skewness[ProbabilityDistribution[
    al be x^(-be - 1) (1 + ga x^-be )^(-(al/ga) - 1) (1 + lam - 2 lam ((1 + ga x^-be )^(-(al/ga)))), {x, 0, ∞}]];
f2[al_, be_, ga_, lam_] = Kurtosis[ProbabilityDistribution[al be x^(-be - 1) (1 + ga x^-be )^(-(al/ga) -  1) (1 + lam - 2 lam ((1 + ga x^-be )^(-(al/ga)))), {x, 
     0, ∞}]];

b = ParametricPlot[{f1[10, be, 1.5, -0.5], f2[10, be, 1.5, -0.5]}, {be, 0.1, 5}];
a = RegionPlot[b2 - (b1)^2 - 1 < 0, {b1, -2, 3}, {b2, 0, 9}];
Show[a, b]

where {al,be,ga} > 0 and lam is between -1 and 1.

But Mathematica is unable to compute skewness and kurtosis of the specified distribution (under this code). How can I compute Skewness and Kurtosis and further plot moments ratio plot of the specified distribution. In above code if I replace ProbabilityDistribution by WeibullDistribution I got moments ratio plot of Weibull distribution.

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