Weibull Distribution Problem Help (Theoretical and Matlab)

**Consider a Weibull distribution with the following pdf: f(x)= (Ɵ2/ Ɵ1)*(x/ Ɵ1)^( Ɵ2-1)*exp{-( x/ Ɵ1)^ Ɵ2}?**

Consider a Weibull distribution with the following pdf:

f(x)= (Ɵ_{2}/ Ɵ_{1})*(x/ Ɵ1)^( Ɵ2-1)*exp{-( x/ Ɵ1)^ Ɵ2} For x>0, Ɵ1>0, Ɵ2>0

(a) if now Y=( x/ Ɵ1)^ Ɵ2. Show that Y follows an exponential distribution with a mean of 1.

Explain how to

(b) Explain how to generate a random variate from this Weibull distribution based on Y.

(c) Use part (a) to generate 500 random variates from this Weibull distribution when (Ɵ1, Ɵ2)=(3,3) and draw a histogram.

(d) Compare the histogram in part (c) with the actual pdf of Weibull (3,3).

(e) Now assume that this Weibull distribution is truncated at points (a,b) = (1,10). Generate 500 random variates from this trunacated Weibull distribution and compute the average.

(f) Compute the (theoretical expected value of this truncated population. Is the average in part(e) close to this expected value?

I am New in statistics and got this question as my homework. I tried my best but not able to solve this. Please help me both in Theoretical as well as Matlab coding for the above question

Re: Weibull Distribution Problem Help (Theoretical and Matlab)

Hey ajmal1075.

Hint: For part (a) Take a look at the exponential PDF compare the PDF when you make the substitution.

Re: Weibull Distribution Problem Help (Theoretical and Matlab)

Please let me know where is the problem arising

Re: Weibull Distribution Problem Help (Theoretical and Matlab)

I'm not sure what you are asking.

Re: Weibull Distribution Problem Help (Theoretical and Matlab)

I compared both PDF and looking OK according to the given condition. Now worry about where is the error

Re: Weibull Distribution Problem Help (Theoretical and Matlab)

Move on to the next one then: all you have to do is show the PDF matches that of Exponential with parameter lambda = 1.

Re: Weibull Distribution Problem Help (Theoretical and Matlab)

Re: Weibull Distribution Problem Help (Theoretical and Matlab)