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The Erlang distribution is a two-parameter family of continuous probability distributions with support x ∈ [ 0 , ∞ ) {\displaystyle x\in [0,\infty )} . The two parameters are:
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Erlang distribution | CDF | P ( k , λ x ) = γ ( k , λ x ) ( k − 1 ) ! = 1 − ∑ n = 0 k − 1 1 n ! e − λ x ( λ x ) n {\displaystyle P(k,\lambda x)={\frac {\gamma (k,\lambda x)}{(k-1)!}}=1-\sum _{n=0}^{k-1}{\f… | 1.00 | infobox |
| Erlang distribution | CF | ( 1 − i t λ ) − k {\displaystyle \left(1-{\frac {it}{\lambda }}\right)^{-k}} | 1.00 | infobox |
| Erlang distribution | Entropy | ( 1 − k ) ψ ( k ) + ln [ Γ ( k ) λ ] + k {\displaystyle (1-k)\psi (k)+\ln \left[{\frac {\Gamma (k)}{\lambda }}\right]+k} | 1.00 | infobox |
| Erlang distribution | Excess kurtosis | 6 k {\displaystyle {\frac {6}{k}}} | 1.00 | infobox |
| Erlang distribution | Mean | k λ {\displaystyle {\frac {k}{\lambda }}} | 1.00 | infobox |
| Erlang distribution | Median | No simple closed form | 1.00 | infobox |
| Erlang distribution | MGF | ( 1 − t λ ) − k {\displaystyle \left(1-{\frac {t}{\lambda }}\right)^{-k}} for t < λ {\displaystyle t<\lambda } | 1.00 | infobox |
| Erlang distribution | Mode | 1 λ ( k − 1 ) {\displaystyle {\frac {1}{\lambda }}(k-1)} | 1.00 | infobox |
| Erlang distribution | Parameters | k ∈ { 1 , 2 , 3 , … } , {\displaystyle k\in \{1,2,3,\ldots \},} shape λ ∈ ( 0 , ∞ ) , {\displaystyle \lambda \in (0,\infty ),} rate alt.: β = 1 / λ , {\displaystyle \beta =1/\la… | 1.00 | infobox |
| Erlang distribution | λ k x k − 1 e − λ x ( k − 1 ) ! {\displaystyle {\frac {\lambda ^{k}x^{k-1}e^{-\lambda x}}{(k-1)!}}} | 1.00 | infobox | |
| Erlang distribution | Skewness | 2 k {\displaystyle {\frac {2}{\sqrt {k}}}} | 1.00 | infobox |
| Erlang distribution | Support | x ∈ [ 0 , ∞ ) {\displaystyle x\in [0,\infty )} | 1.00 | infobox |
| Erlang distribution | Variance | k λ 2 {\displaystyle {\frac {k}{\lambda ^{2}}}} | 1.00 | infobox |
| Erlang distribution | is a | two-parameter family of continuous probability distributions with support x | 0.90 | text |
| Erlang distribution | is a | distribution of a sum of k | 0.90 | text |
| Erlang distribution | is a | special case of the gamma distribution in which the shape of the distribution is discretized.The Erlang distribution was developed by A | 0.90 | text |
| Erlang distribution | is a | distribution of the sum of k independent and identically distributed random variables | 0.90 | text |
| Erlang distribution | is a | special case of the Pearson type III distribution | 0.90 | text |
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