Indicators {\ displaystyle k> 0 \,} (real)

{\ displaystyle \ theta> 0 \,} (real)

Support {\ displaystyle x \ in [0, \ infty) \!}

KD. {\ displaystyle x ^ {k-1} {\ frac {\ exp {\ left (-x / \ theta \ right)}} {\ Gamma (k) \, \ theta ^ {k}}} \, \! }

DT {= {\ displaystyle {\ frac {\ gamma (k, x / \ theta)} {\ Gamma (k)}} \!}

The arithmetic mean {\ displaystyle k \ theta \!}

The arithmetic mean without a simple closed formula.

{\ Displaystyle (k-1) \ theta {{text {for}} k \ geq 1 \, \!}

Contrast {\ displaystyle k \ theta ^ {2} \, \!}

{\ Displaystyle {\ frac {2} {\ sqrt {k}}} \, \!}

{{Displaystyle {\ frac {6} {k}} \, \!}

{\ Displaystyle k + \ ln \ theta + \ ln \ Gamma (k) \!}

{\ displaystyle + (1-k) \ psi (k) \!}

DM {\ displaystyle (1- \ theta \, t) ^ {- k} {\ text {for}} t

Dear Ali,

Thank you for your participation.

Regards

Did you try to use TBSSurvival R Package? It might help you:

https://cran.r-project.org/web/packages/TBSSurvival/vignettes/TBSSurvival.pdf