corrTP | R Documentation |

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

corrTP(dist, corr, dist.par)

`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. |

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*.

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

Araújo A, Meira-Machado L, Roca-Pardiñas J (2014). TPmsm: Estimation of the Transition Probabilities in
3-State Models. *Journal of Statistical Software*, **62**(4), 1-29. doi: 10.18637/jss.v062.i04

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. doi: 10.1007/BF00049307

`dgpTP`

.

# 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))

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.