mletype1 {bccp} | R Documentation |

## Computing the maximum likelihood estimator (MLE) for the parameters of the statistical model fitted to a progressive type-I interval censoring scheme.

### Description

Computes the MLE of for the parameters of the model fitted to a progressive type-I interval censoring scheme with likelihood function

`l(\Theta)=\log L(\Theta) \propto \sum_{i=1}^{m}X_i \log \bigl[F(t_{i}{{;}}\Theta)-F(t_{i-1}{{;}}\Theta)\bigr]+\sum_{i=1}^{m}R_i\bigl[1-F(t_{i}{{;}}\Theta)\bigr],`

in which `F(.;\Theta)`

is the family cumulative distribution function for `\Theta=(\theta_1,\dots,\theta_k)^T`

provided that
`F(t_{0};\Theta)=0`

.

### Usage

```
mletype1(plan, param, start, cdf.expression = FALSE, pdf.expression = TRUE, cdf, pdf,
method = "Nelder-Mead", lb = 0, ub = Inf, level = 0.05)
```

### Arguments

`plan` |
Censoring plan for progressive type-I interval censoring scheme. It must be given as a |

`param` |
Vector of the of the family parameter's names. |

`start` |
Vector of the initial values. |

`cdf.expression` |
Logical. That is |

`pdf.expression` |
Logical. That is |

`cdf` |
Expression of the cumulative distribution function. |

`pdf` |
Expression of the probability density function. |

`method` |
The method for the numerically optimization that includes one of |

`lb` |
Lower bound of the family's support. That is zero by default. |

`ub` |
Upper bound of the family's support. That is |

`level` |
Significance level for constructing asymptotic confidence interval That is |

### Value

MLE, standard error of MLE, and asymptotic confidence interval for MLE.

### Author(s)

Mahdi Teimouri

### Examples

```
data(plasma, package="bccp")
plan <- data.frame(T = plasma$upper, X = plasma$X, P = plasma$P, R = plasma$R)
param <- c("lambda","beta")
mle <- c(1.4, 0.05)
pdf <- quote( lambda*(1-exp( -(x*beta)))^(lambda-1)*beta*exp( -(x*beta)) )
cdf <- quote( (1-exp( -(x*beta)))^lambda )
lb <- 0
ub <- Inf
level <- 0.05
mletype1(plan = plan, param = param, start = mle, cdf.expression = FALSE, pdf.expression = TRUE,
cdf = cdf, pdf = pdf, method = "Nelder-Mead", lb = lb, ub = ub, level = level)
```

*bccp*version 0.5.0 Index]