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# Erlang Distribution

## Parameters

- shape parameter (positive integer)
- continuous scale parameter ()
- continuous location parameter ( yields the two-parameter Erlang distribution)

## Two-Parameter Erlang Distribution

### Cumulative Distribution Function

where is the Gamma Function,  and is the Incomplete Gamma Function.

## Worksheet and VBA Functions

The following worksheet and VBA functions are available for this distribution:

 Description VBA Functions Worksheet Functions Distribution Fitting - ``` =DistFit("Erlang";Data;[Options]```1```) ``` Probability Density Function `ErlangPdf(x,m,beta,[gamma])` ``` =ErlangPdf(m;beta;[gamma]) =DistPdf("Erlang(m;beta;[gamma])";x) ``` Cumulative Distribution Function `ErlangCdf(x,m,beta,[gamma])` ``` =ErlangCdf(m;beta;[gamma]) =DistCdf("Erlang(m;beta;[gamma])";x) ``` Survival Function `ErlangSurv(x,m,beta,[gamma])` ``` =DistSurv("Erlang(m;beta;[gamma])";x) ``` Hazard Function `ErlangHaz(x,m,beta,[gamma])` ``` =ErlangHaz(m;beta;[gamma]) =DistHaz("Erlang(m;beta;[gamma])";x) ``` Cumulative Hazard Function `ErlangCumHaz(x,m,beta,[gamma])` ``` =DistCumHaz("Erlang(m;beta;[gamma])";x) ``` Inverse CDF (Quantile Function) `ErlangInv(P,m,beta,[gamma])` ``` =ErlangInv(m;beta;[gamma]) =DistInv("Erlang(m;beta;[gamma])";P) ``` Random Numbers `ErlangRand(m,beta,[gamma])` ``` =ErlangRand(m;beta;[gamma]) =DistRand("Erlang(m;beta;[gamma])") ``` Mode `ErlangMode(m,beta,[gamma])` ``` =DistMode("Erlang(m;beta;[gamma])") ``` Mean `ErlangMean(m,beta,[gamma])` ``` =ErlangMean(m;beta;[gamma]) =DistMean("Erlang(m;beta;[gamma])") ``` Variance `ErlangVar(m,beta,[gamma])` ``` =ErlangVar(m;beta;[gamma]) =DistVar("Erlang(m;beta;[gamma])") ``` Standard Deviation `ErlangStdev(m,beta,[gamma])` ``` =ErlangStdev(m;beta;[gamma]) =DistStdev("Erlang(m;beta;[gamma])") ``` Skewness `ErlangSkew(m,beta,[gamma])` ``` =DistSkew("Erlang(m;beta;[gamma])") ``` (Excess) Kurtosis `ErlangKurt(m,beta,[gamma])` ``` =DistKurt("Erlang(m;beta;[gamma])") ```

1. The `Options` parameter is optional. Possible options: "gamma=value"  (example: "gamma=0")
2. The `gamma` parameter is optional (the default value is 0).