fit.binomialLogitnorm {QRMlib}R Documentation

Fit Logitnormal-Binomial Distribution

Description

fits a mixed binomial distribution where success probability has a logitnormal distribution This function has been altered in the R-language edition to contain two extra parameters providing upper and lower limits for the input parameters M and m. if convergence occurs at an endpoint of either limit, you need to reset lower and upper parameter estimators and run the function again

Usage

fit.binomialLogitnorm(M, m, startvals=c(-1, 0.5), 
lowerParamLimits = c(-5.0, 0.02), upperParamLimits = c(1,0.9))

Arguments

M vector of numbers of successes (e.g. number of defaults in a credit-rating class)
m vector of numbers of trials (e.g. number of obligors in a credit-rating class)
startvals starting values for parameter estimates
lowerParamLimits vector with lower limits for each parameter to be used by optimization algorithm
upperParamLimits vector with upper limits for each parameter to be used by optimization algorithm

Details

This function calls the R-language method optim(...method="L-BFGS-B") which uses input parameter vectors of upper and lower limits. Hence if convergence occurs at an endpoint of either limit, you may need to expand the corresponding upper or lower limit and run the function again.

Value

list containing parameter estimates and details of fit:

par.ests vector of optimum parameter estimators
maxloglik value of likelihood function at optimum
converged T or F indicating convergence
details any messages associated with convergence algorithm
pi probability of a single default (see p. 345 in QRM)
pi2 probability of two joint defaults (see p. 345 in QRM)
rhoY default correlation (see p. 345 in QRM)

Author(s)

documentation by Scott Ulman for R-language distribution

See Also

fit.binomial, fit.binomialBeta, fit.binomialProbitnorm

Examples

data(spdata.raw); 
attach(spdata.raw); 
BdefaultRate <- Bdefaults/Bobligors; 
# A little patience is required for the next model ... 
mod3 <- fit.binomialLogitnorm(Bdefaults, Bobligors); 

[Package QRMlib version 1.4.4 Index]