Dear Colleagues,
I will be grateful if you help me by referring to some references about Estimating the reliability function of Gamma distribution.
Thanks in advance.
Huda
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
Did you try to use TBSSurvival R Package? It might help you:
https://cran.r-project.org/web/packages/TBSSurvival/vignettes/TBSSurvival.pdf
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