Noncentral F-ratio distribution with PDF Mean and Variance
NoncentralFRatioDistribution[n, m, λ]
NoncentralFRatioDistribution[n, m, λ, η]
Mean[NoncentralFRatioDistribution[n, m, λ]]
→ Piecewise[{{(m*(n + λ))/((-2 + m)*n), m > 2}}, Indeterminate]PDF[NoncentralFRatioDistribution[n, m, λ], x]
→ Piecewise[{{(m^(m/2)*n^(n/2)*x^((-2 + n)/2)*(m + n*x)^((-m - n)/2)*Hypergeometric1F1[(m + n)/2, n/2, (n*x*λ)/(2*(m + n*x))])/(E^(λ/2)*Beta[n/2, m/2]), x > 0}}, 0]Variance[NoncentralFRatioDistribution[n, m, λ]]
→ Piecewise[{{(2*m^2*((-2 + m)*(n + 2*λ) + (n + λ)^2))/((-4 + m)*(-2 + m)^2*n^2), m > 4}}, Indeterminate]