Trivial Question on Gamma Distribution Function

[I_am_learning]

If a random variable X follows Gamma Distribution Function with parameters K and thita, what does (X+k) follow? if K is a constant.
I think, since adding the constant is just like shifting the origin, the nature of the curve remain unchanged. But what about its parameter?
Thanks.

 

[micromass]

Let X be the standard gamma distribution with parameter \alpha. Then this has pdf

p_X(x)=\frac{1}{\Gamma (\alpha)}x^{\alpha-1} e^{-x}

for x>0. Then we define the generalized gamma distribution as Y=a+\lambda X. This has pdf

P_Y(x)=\frac{1}{\Gamma(\alpha)\lambda^\alpha}(x-a)^{\alpha-1}e^{-(x-a)/\lambda}

if x>a. This is the \Gamma(\alpha,a,\lambda)-distribution. The standard gamma is \Gamma(\alpha,0,1). So to answer your question:

if Y\sim \Gamma(\alpha,a,\lambda), then Y+k\sim \Gamma(\alpha,a+k,\lambda).

 

[I_am_learning]

Thank you for your kind help.