chat_pois {SimMultiCorrData}

Calculate Upper Frechet-Hoeffding Correlation Bound: Poisson - Normal Variables

Description

This function calculates the upper Frechet-Hoeffding bound on the correlation between a Poisson variable and the normal variable used to generate it. It is used in findintercorr_cat_pois and findintercorr_cont_pois in calculating the intermediate MVN correlations. This uses the method of Amatya & Demirtas (2015, doi: 10.1080/00949655.2014.953534). This function would not ordinarily be called directly by the user.

Usage

chat_pois(lam, n_unif = 10000, seed = 1234)

Arguments

lam

a vector of lambda (> 0) constants for the Poisson variables (see Poisson)

n_unif

the number of uniform random numbers to generate in calculating the bound (default = 10000)

seed

the seed used in random number generation (default = 1234)

Value

A scalar equal to the correlation upper bound.

References

Amatya A & Demirtas H (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 85(15): 3129-39. doi: 10.1080/00949655.2014.953534.

Demirtas H & Hedeker D (2011). A practical way for computing approximate lower and upper correlation bounds. American Statistician, 65(2): 104-109. doi: 10.1198/tast.2011.10090.

Frechet M. Sur les tableaux de correlation dont les marges sont donnees. Ann. l'Univ. Lyon SectA. 1951;14:53-77.

Hoeffding W. Scale-invariant correlation theory. In: Fisher NI, Sen PK, editors. The collected works of Wassily Hoeffding. New York: Springer-Verlag; 1994. p. 57-107.

Yahav I & Shmueli G (2012). On Generating Multivariate Poisson Data in Management Science Applications. Applied Stochastic Models in Business and Industry, 28(1): 91-102. doi: 10.1002/asmb.901.

See Also

findintercorr_cat_pois, findintercorr_cont_pois, findintercorr