Comparing the Exponential Truncated Distribution with the Exponential Distribution
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I have the truncated exponential distribution: $$f(x)=frac{lambda e^{-lambda x}}{1-e^{-lambda k }} quad text{ for } 0 <x<k$$ The expected value of this for $k=frac{lambda}{5}$ is $$frac{1}{lambda}(1-frac{5}{e^5-1})$$ I'm trying to compare this expected value with the expected value of the exponential distribution with parameter $lambda$ and all I can see is that it's just smaller by a factor of $(1-frac{5}{e^5-1})$. I'm wondering if there's anything more that this relation between their expected values reveals other than the truncated exponential distribution has a smaller expected value.
exponential-distribution
asked Nov 19 at 11:22
Hai
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I have the truncated exponential distribution: $$f(x)=frac{lambda e^{-lambda x}}{1-e^{-lambda k }} quad text{ for } 0 <x<k$$ The expected value of this for $k=frac{lambda}{5}$ is $$frac{1}{lambda}(1-frac{5}{e^5-1})$$ I'm trying to compare this expected value with the expected value of the exponential distribution with parameter $lambda$ and all I can see is that it's just smaller by a factor of $(1-frac{5}{e^5-1})$. I'm wondering if there's anything more that this relation between their expected values reveals other than the truncated exponential distribution has a smaller expected value.
exponential-distribution
asked Nov 19 at 11:22
Hai
1379
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have the truncated exponential distribution: $$f(x)=frac{lambda e^{-lambda x}}{1-e^{-lambda k }} quad text{ for } 0 <x<k$$ The expected value of this for $k=frac{lambda}{5}$ is $$frac{1}{lambda}(1-frac{5}{e^5-1})$$ I'm trying to compare this expected value with the expected value of the exponential distribution with parameter $lambda$ and all I can see is that it's just smaller by a factor of $(1-frac{5}{e^5-1})$. I'm wondering if there's anything more that this relation between their expected values reveals other than the truncated exponential distribution has a smaller expected value.
exponential-distribution
asked Nov 19 at 11:22
Hai
1379
I have the truncated exponential distribution: $$f(x)=frac{lambda e^{-lambda x}}{1-e^{-lambda k }} quad text{ for } 0 <x<k$$ The expected value of this for $k=frac{lambda}{5}$ is $$frac{1}{lambda}(1-frac{5}{e^5-1})$$ I'm trying to compare this expected value with the expected value of the exponential distribution with parameter $lambda$ and all I can see is that it's just smaller by a factor of $(1-frac{5}{e^5-1})$. I'm wondering if there's anything more that this relation between their expected values reveals other than the truncated exponential distribution has a smaller expected value.
exponential-distribution
exponential-distribution
asked Nov 19 at 11:22
Hai
1379
asked Nov 19 at 11:22
Hai
1379
asked Nov 19 at 11:22
Hai
1379
asked Nov 19 at 11:22
Hai
1379
asked Nov 19 at 11:22
Hai
1379
1379
add a comment |
add a comment |
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