- #1
mcguiry03
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Homework Statement
prove that,
for gamma distribution
μ=αθ
σ^2=αθ^2
for exponential distribution
μ=θ
σ^2=θ^2
mcguiry03 said:Homework Statement
prove that,
for gamma distribution
μ=αθ
σ^2=αθ^2
for exponential distribution
μ=θ
σ^2=θ^2
Gamma distribution is a continuous probability distribution that is used to model the time required for multiple events to occur. Exponential distribution, on the other hand, is used to model the time between events in a Poisson process. In other words, gamma distribution is used to model the total time for a certain number of events, while exponential distribution models the time between each event.
Gamma distribution is a generalization of chi-squared distribution. In fact, when the shape parameter of a gamma distribution is an integer, it is equivalent to a chi-squared distribution with the same shape parameter.
The mean of a gamma distribution is equal to the shape parameter divided by the rate parameter. The variance is equal to the shape parameter divided by the square of the rate parameter.
Exponential distribution is commonly used in reliability analysis to model the failure rate of a system. It is used to calculate the probability of failure within a certain time period, given the failure rate of the system.
Gamma distribution has various applications in fields such as finance, economics, and engineering, where it is used to model waiting times or durations. Exponential distribution is commonly used in reliability analysis, but it also has applications in areas such as queuing theory, telecommunication, and population studies.