bivgeom (version 1.0)

lambda1Roy: Bivariate failure rates

Description

Bivariate failure rate \(\lambda_1\)

Usage

lambda1Roy(x, y, theta1, theta2, theta3)

Arguments

x

observation from the first variable

y

observation from the second variable

theta1

paramater \(\theta_1\)

theta2

paramater \(\theta_2\)

theta3

paramater \(\theta_3\)

Value

Value of the bivariate failure rate \(\lambda_1\) for Roy's bivariate geometric model (Roy, 1993)

Details

It is defined as \(P(X=x,Y\geq y)/P(X\geq x,Y\geq y)\). For this model, \(\lambda_1(x,y)=1-\theta_1\theta_3^y\)

References

Roy, D. (1993) Reliability measures in the discrete bivariate set-up and related characterization results for a bivariate geometric distribution, Journal of Multivariate Analysis 46(2), 362-373.

See Also

lambda2Roy

Examples

# NOT RUN {
theta1 <- 0.5
theta2 <- 0.7
theta3 <- 0.9
# bivariate failure rate lambda1
# computed in x=1, y=2
x <- 1
y <- 2
lambda1Roy(x,y,theta1,theta2,theta3)
# }