Erlang Distribution

Parameters

Domain

Three-Parameter Erlang Distribution

Probability Density Function

Cumulative Distribution Function

Two-Parameter Erlang Distribution

Probability Density Function

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).