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Integration Program of Burr Distribution

• To: mathgroup at smc.vnet.net
• Subject: [mg91545] Integration Program of Burr Distribution
• From: "Dewi Anggraini" <dewi_anggraini at student.rmit.edu.au>
• Date: Tue, 26 Aug 2008 03:30:09 -0400 (EDT)

Dear All

I'd like to calculate the upper specification limit of Burr Distribution from my data below:

n = 69;
x1 = {3, 5, 6, 14, 11, 7, 7, 10, 11, 5, 4, 19, 9, 2, 8, 5, 6, 6, 5,
   5,
       4, 5, 5, 6, 8, 5, 8, 6, 5, 16, 5, 18, 16, 21, 6, 3, 16, 8, 3,
   8,
       11, 2, 3, 4, 8, 7, 9, 10, 8, 11, 8, 10, 9, 12, 12, 9, 6, 12,
   3, 9,
       14, 7, 4, 13, 8, 14, 5, 8, 2};

with the initialisation pdf of Burr as follows:

BurrDistribution[x1_, c_,
  k_] := (c*k)*(x1^(c - 1)/(1 + x1^c)^(k + 1))
pdf = BurrDistribution[x1, c, k]

I already got the parameter value of c and k through MLE:

logl = Plus @@ Log[pdf]
maxlogl = FindMinimum[{-logl, c > 0 && k > 0}, {c, 1}, {k, 2},
     MaxIterations -> 1000]
mle = maxlogl[[2]]

However, when I wanna calculate the integration of Burr with the value of c=37.8115, k=0.0135614 and x1 limit = [8, Infinity] to get the probability of data fall outside the upper specification limit given {8} with this program below:

In[2]:= Integrate[pdf[37.81151579009424, 0.01356141249769735, t], 
   {t, 8, Infinity}]

Out[2]= Integrate[pdf[37.81151579009424, 0.01356141249769735, t], 
   {t, 8, Infinity}]

That gives me the repetation not a real number.

Why is this happen? Do I make mistake somewhere? Because when I did the similar program towards Gamma Distribution, it works well.

I look forward for your reply and assistance. I highly appreciate the suggestions you contribute to my minor thesis.

Thank You.
Regards,
Dewi

• Follow-Ups:
  • Re: Integration Program of Burr Distribution
    • From: Daniel Lichtblau <danl@wolfram.com>