Erlang distribution

What Erlang distribution is

The Erlang Distribution is a special type of continuous probability distribution that is used to model the time it takes for events to occur. It is often used in queueing theory to model the distribution of job completion times.

Steps for “Erlang Distribution”:

  1. Determine the mean (μ) and shape parameter (k) of the Erlang distribution.

  2. Calculate the variance (σ2) of the Erlang distribution using the formula σ2=μ2/k.

  3. Calculate the cumulative distribution function (CDF) of the Erlang distribution using the formula CDF(x)=1-e-x/μ*((x/μ)^k-1)/k!.

  4. Calculate the probability density function (PDF) of the Erlang distribution using the formula PDF(x)=e-x/μ*(x/μ)^(k-1)/(μ^k*k!).

  5. Calculate the moment generating function (MGF) of the Erlang distribution using the formula MGF(t)=e^(μt)((1-t/μ)^(-k)).

Examples

  1. Erlang distribution is often used to model the distribution of call times in a call center.

  2. Erlang distribution is sometimes used to model the probability of an event occurring a certain number of times within a fixed time interval.

  3. Erlang distribution is sometimes used to estimate the reliability of a system by modeling the time between successive failures.

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