estbivgeomRoy {bivgeom} R Documentation

## Parameter estimation

### Description

Parameter estimation for Roy's bivariate geometric model

### Usage

```estbivgeomRoy(x, y, method = "LS")
```

### Arguments

 `x` vector of observations from the first variable X `y` vector of observations from the first variable y, same length as `x` `method` One of the possible estimation methods: "ML" (maximum likelihood), "LS" (least squares), "MMP" (method of moment and poroportion), "M1", "M2", "M3", and "M4" (several variants of the method of moments)

### Value

a vector of length 3 containing the estimates of theta_1, theta_2, and theta_3

### Author(s)

Alessandro Barbiero

### References

Barbiero, A. (2018) Properties and estimation of a bivariate geometric model with locally constant failure rates, submitted

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

`dbivgeomRoy`, `minuslogRoy`

### Examples

```theta1 <- 0.5
theta2 <- 0.7
theta3 <- 0.9
# random sample of size n=1000:
set.seed(12345)
n <- 1000
d <- rbivgeomRoy(n, theta1, theta2, theta3)
# parameter estimation, using the different proposed methods:
hattheta <- estbivgeomRoy(d[,1], d[,2], "ML")
hattheta # MLEs
estbivgeomRoy(d[,1], d[,2], "LS")
estbivgeomRoy(d[,1], d[,2], "MMP")
```

[Package bivgeom version 1.0 Index]