corrTP: Correlation between two gap times

Description Usage Arguments Details Author(s) References See Also Examples

View source: R/corrTP.R

Description

Provides the correlation between the bivariate times for some copula distributions.

Usage

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corrTP(dist, corr, dist.par)

Arguments

dist

The distribution. Possible bivariate distributions are “exponential” and “weibull”.

corr

Correlation parameter. Possible values for the bivariate exponential distribution are between -1 and 1 (0 for independency). Any value between 0 (not included) and 1 (1 for independency) is accepted for the bivariate Weibull distribution.

dist.par

Vector of parameters for the allowed distributions. Two (scale) parameters for the bivariate exponential distribution and four (2 location parameters and 2 scale parameters) for the bivariate Weibull distribution. See details below.

Details

The bivariate exponential distribution, also known as Farlie-Gumbel-Morgenstern distribution is given by

F(x,y)=F_1(x)F_2(y)[1+α(1-F_1(x))(1-F_2(y))]

for x≥0 and y≥0. Where the marginal distribution functions F_1 and F_2 are exponential with scale parameters θ_1 and θ_2 and correlation parameter α, -1 ≤ α ≤ 1.

The bivariate Weibull distribution with two-parameter marginal distributions. It's survival function is given by

S(x,y)=P(X>x,Y>y)=exp^(-[(x/θ_1)^(β_1/δ)+(y/θ_2)^(β_2/δ)]^δ)

Where 0 < δ ≤ 1 and each marginal distribution has shape parameter β_i and a scale parameter θ_i, i = 1, 2.

Author(s)

Artur Araújo, Javier Roca-Pardiñas and Luís Meira-Machado

References

Johnson N., Kotz S. (1972) Distributions in statistics: continuous multivariate distributions John Wiley and Sons.

Lu J., Bhattacharya G. (1990) Some new constructions of bivariate weibull models. Annals of Institute of Statistical Mathematics 42(3), 543–559.

See Also

dgpTP.

Examples

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# Example for the bivariate Weibull distribution
corrTP(dist = "weibull", corr = 0.5, dist.par = c(2, 7, 2, 7))

# Example for the bivariate Exponential distribution
corrTP(dist = "exponential", corr = 1, dist.par = c(1, 1))

TPmsm documentation built on Aug. 5, 2019, 1:02 a.m.