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enter image description hereenter image description hereenter image description hereHow to draw the Lorenz (𝐿𝐹 (𝑡)) and Bonferroni (𝐵𝐹 (𝑡)) curves for the given distribution with 3D version with interpretation with varying parameters, and when the CDF of the distribution does not have a closed form expression enter image description here f[[Eta], [Omega], [Delta]_] :=

ProbabilityDistribution[(

E^(-2 *x*\[Eta] - 

x^\[Delta]* \[Omega]) (4 *x^2 *\[Eta]^2 + 

x^\[Delta] *\[Delta] *\[Omega] + 

2 *x^(1 + \[Delta]) \[Eta] *\[Delta]* \[Omega]))/

x, {x, 0, \[Infinity]},

Assumptions -> \[Eta] > 0 && \[Omega] > 0 && \[Delta] > 0];

PDF[f[\[Eta], \[Omega], \[Delta]], x];
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  • $\begingroup$ Write what integral you want to solve? $\endgroup$
    – Mariusz Iwaniuk
    Commented Jun 23 at 10:50
  • $\begingroup$ @MariuszIwaniuk have mentioned both of the functions which I want to plot $\endgroup$
    – Sid
    Commented Jun 23 at 18:40
  • $\begingroup$ What is f(t) ? $\endgroup$
    – Mariusz Iwaniuk
    Commented Jun 23 at 18:55
  • $\begingroup$ There is a closed-form for the CDF: cdf = Simplify[CDF[f[\[Eta], \[Omega], \[Delta]], x], x > 0] which results in $e^{-\omega x^{\delta }-2 \eta x} \left(e^{\omega x^{\delta }+2 \eta x}-2 \eta x-1\right)$. And if you set $\delta$ to specific integer values, you get a closed-form result. $\endgroup$
    – JimB
    Commented Jun 23 at 23:26
  • $\begingroup$ Than you @JimB I have got the same form of the CDF but its quantile form is not in closed form actually i have to mention that quantile function not CDF. Thank you for the help. $\endgroup$
    – Sid
    Commented Jun 24 at 6:31

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