Dataset: ConductorFailureTimes

Description

This dataset contains failure times measured in hours from an accelerated life test with 59 conductors.

Usage

data(ConductorFailureTimes)

Format

A numeric vector of failure times.

Details

This dataset contains failure times (measured in hours) obtained from an accelerated life test involving 59 conductors. The data are presented as a numeric vector.

References

Nasiri, B., et al. (2010). "Bayesian analysis of the accelerated life model with Type-II censoring." Journal of Statistical Planning and Inference, 140(6), 1565-1572.

Schafft, H. A., et al. (1987). "Reproducibility of the accelerated test for electric cable insulation." IEEE Transactions on Electrical Insulation, 22(5), 739-746.

Dataset: Tree_diameters

Description

This dataset contains tree diameter measurements (in cm) for Teak trees in the Agrimey sector in Benin.

Usage

data(Tree_diameters)

Format

A numeric vector of tree diameter measurements (in cm).

Cumulative Distribution Function (CDF) for the TLCAR Distribution

Description

Calculate the cumulative distribution at a given value using the TLCAR distribution.

Usage

cTLCAR(x, alpha, a, b, theta, m)

Arguments

Details

The cumulative distribution function (CDF) for the TLCAR distribution is defined as follows:

F(x)=\left[ 1-\left(\frac{1}{2}-\frac{1}{\pi}\arctan\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right) -b}{a}\right)^2\right]^\alpha

Value

Cumulative distribution at the given value.

Examples

cTLCAR(x = 1, alpha = 1, a = 1, b = 0, theta = 2, m = 0.5)

Probability Density Function (PDF) for the TLCAR Distribution

Description

Calculate the probability density at a given value using the TLCAR distribution.

Usage

dTLCAR(x, alpha, a, b, theta, m)

Arguments

Details

The probability density function (PDF) for the TLCAR distribution is defined as follows:

f(x)=\frac{2\alpha}{\pi a}\left[\frac{1+\left(\frac{x^2}{\theta^2}-1\right)e^{-\frac{x^2}{2\theta^2}}+m}{1+\left(\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right) -b}{a}\right)^2}\right]\left[\frac{1}{2}-\frac{1}{\pi}\arctan\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right) -b}{a}\right]\left[ 1-\left(\frac{1}{2}-\frac{1}{\pi}\arctan\frac{x\left(1-e^{-\frac{x^2}{2\theta^2}}+m\right)-b}{a}\right)^2\right]^{\alpha-1}

Value

Probability density at the given value.

Examples

dTLCAR(x = 1, alpha = 1, a = 1, b = 0, theta = 2, m = 0.5)

Estimate parameters for the TLCAR distribution using maximum likelihood.

Description

This function estimates the parameters of the TLCAR distribution while respecting the constraints on the parameters.

Usage

fTLCAR(data)

Arguments

Value

Numeric vector of estimated parameters.

Examples

data(ConductorFailureTimes)
estimated_params <- fTLCAR(ConductorFailureTimes)

Graphical Plot of the TLCAR Distribution

Description

Generate a graphical plot of the probability density function (PDF) or cumulative distribution function (CDF) for the TLCAR distribution.

Usage

ploTLCAR(x, alpha, a, b, theta, m, type = "pdf")

Arguments

Value

A graphical plot of the TLCAR distribution.

Examples

ploTLCAR(x = seq(0, 10, by = 0.1), alpha = 0.5, a = 1, b = 0, theta = 2, m = 1, type = "pdf")

Quantile function for TLCAR distribution

Description

Calculate the quantile value for a given probability using the TLCAR distribution.

Usage

qTLCAR(p, alpha, a, b, theta, m)

Arguments

Value

Numeric value representing the quantile.

Examples

 qTLCAR(p = 0.5, alpha = 1, a = 1, b = 0, theta = 3, m = 1)

Generate a random sample from the TLCAR distribution

Description

Generate a random sample from the TLCAR distribution using the quantile function.

Usage

rTLCAR(n, alpha, a, b, theta, m)

Arguments

Value

Random sample from the TLCAR distribution.

Examples

# Generate a random sample with 100 observations using estimated parameters
sample <- rTLCAR(n = 100, alpha = 1, a = 1, b = 0, theta = 3, m = 1)

Estimate parameters with constraints and plot histogram with estimated density

Description

This function estimates the parameters of the TLCAR distribution while respecting the constraints on the parameters. It plots the histogram of the data along with the estimated density curve.

Usage

sTLCAR(data)

Arguments

Value

Numeric vector of estimated parameters.

Examples

data(ConductorFailureTimes)
sTLCAR(ConductorFailureTimes)

Temporary Variable Calculation

Description

This function calculates a temporary variable used in the TLCAR distribution density function.

Usage

temp_var(x, theta, a, b, m)

Arguments

Value

Numeric vector of calculated temporary variable values