Hyper-Erlang distribution - Misplaced Pages

Continuous probability distribution

In probability theory, a hyper-Erlang distribution is a continuous probability distribution which takes a particular Erlang distribution E_i with probability p_i. A hyper-Erlang distributed random variable X has a probability density function given by

A(x)=\sum _{i=1}^{n}p_{i}E_{l_{i}}(x)

where each p_i > 0 with the p_i summing to 1 and each of the E_{l_i} being an Erlang distribution with l_i stages each of which has parameter λ_i.

References

Bocharov, P. P.; D'Apice, C.; Pechinkin, A. V. (2003). "2. Defining parameters of queueing systems". Queueing Theory. doi:10.1515/9783110936025.61. ISBN 9783110936025.
Yuguang Fang; Chlamtac, I. (1999). "Teletraffic analysis and mobility modeling of PCS networks". IEEE Transactions on Communications. 47 (7): 1062. doi:10.1109/26.774856.
Fang, Y. (2001). "Hyper-Erlang Distribution Model and its Application in Wireless Mobile Networks". Wireless Networks. 7 (3). Kluwer Academic Publishers: 211–219. doi:10.1023/A:1016617904269.

Probability distributions (list)

Discrete
univariate

with finite support	Benford Bernoulli Beta-binomial Binomial Categorical Hypergeometric Negative Poisson binomial Rademacher Soliton Discrete uniform Zipf Zipf–Mandelbrot
with infinite support	Beta negative binomial Borel Conway–Maxwell–Poisson Discrete phase-type Delaporte Extended negative binomial Flory–Schulz Gauss–Kuzmin Geometric Logarithmic Mixed Poisson Negative binomial Panjer Parabolic fractal Poisson Skellam Yule–Simon Zeta

Continuous
univariate

supported on a bounded interval	Arcsine ARGUS Balding–Nichols Bates Beta Generalized Beta rectangular Continuous Bernoulli Irwin–Hall Kumaraswamy Logit-normal Noncentral beta PERT Raised cosine Reciprocal Triangular U-quadratic Uniform Wigner semicircle
supported on a semi-infinite interval	Benini Benktander 1st kind Benktander 2nd kind Beta prime Burr Chi Chi-squared Noncentral Inverse Scaled Dagum Davis Erlang Hyper Exponential Hyperexponential Hypoexponential Logarithmic F Noncentral Folded normal Fréchet Gamma Generalized Inverse gamma/Gompertz Gompertz Shifted Half-logistic Half-normal Hotelling's T-squared Inverse Gaussian Generalized Kolmogorov Lévy Log-Cauchy Log-Laplace Log-logistic Log-normal Log-t Lomax Matrix-exponential Maxwell–Boltzmann Maxwell–Jüttner Mittag-Leffler Nakagami Pareto Phase-type Poly-Weibull Rayleigh Relativistic Breit–Wigner Rice Truncated normal type-2 Gumbel Weibull Discrete Wilks's lambda
supported on the whole real line	Cauchy Exponential power Fisher's z Kaniadakis κ-Gaussian Gaussian q Generalized normal Generalized hyperbolic Geometric stable Gumbel Holtsmark Hyperbolic secant Johnson's S_U Landau Laplace Asymmetric Logistic Noncentral t Normal (Gaussian) Normal-inverse Gaussian Skew normal Slash Stable Student's t Tracy–Widom Variance-gamma Voigt
with support whose type varies	Generalized chi-squared Generalized extreme value Generalized Pareto Marchenko–Pastur Kaniadakis κ-exponential Kaniadakis κ-Gamma Kaniadakis κ-Weibull Kaniadakis κ-Logistic Kaniadakis κ-Erlang q-exponential q-Gaussian q-Weibull Shifted log-logistic Tukey lambda

Mixed
univariate

continuous- discrete	Rectified Gaussian

Multivariate
(joint)

Discrete:
Ewens
Multinomial
- Dirichlet
- Negative
Continuous:
Dirichlet
- Generalized
Multivariate Laplace
Multivariate normal
Multivariate stable
Multivariate t
Normal-gamma
- Inverse
Matrix-valued:
LKJ
Matrix beta
Matrix normal
Matrix t
Matrix gamma
- Inverse
Wishart
- Normal
- Inverse
- Normal-inverse
- Complex

Directional

Univariate (circular) directional: Circular uniform; Univariate von Mises; Wrapped normal; Wrapped Cauchy; Wrapped exponential; Wrapped asymmetric Laplace; Wrapped Lévy
Bivariate (spherical): Kent
Bivariate (toroidal): Bivariate von Mises
Multivariate: von Mises–Fisher; Bingham

Degenerate
and singular

Degenerate: Dirac delta function
Singular: Cantor

Families

Category:

Continuous distributions

See also

References