CEEBio distribution {ComRiskModel} | R Documentation |

## Complementary exponentiated exponential binomial distribution

### Description

Evaluates the PDF, CDF, QF, random numbers and MLEs based on the complementary exponentiated exponential binomial (CEEBio) distribution. The CDF of the complementary G binomial distribution is as follows:

```
F(x)=\frac{\left[1-\lambda(1-G(x))\right]^{m}-(1-\lambda)^{m}}{1-(1-\lambda)^{m}};\qquad\lambda\in\left(0,1\right),\,m\geq1,
```

where G(x) represents the baseline exponentiated exponential CDF, it is given by

```
G(x)=\left(1-\exp(-\alpha x)\right)^{\beta};\qquad\alpha,\beta>0.
```

By setting G(x) in the above Equation, yields the CDF of the CEEBio distribution.

### Usage

```
dCEEBio(x, alpha, beta, m, lambda, log = FALSE)
pCEEBio(x, alpha, beta, m, lambda, log.p = FALSE, lower.tail = TRUE)
qCEEBio(p, alpha, beta, m, lambda, log.p = FALSE, lower.tail = TRUE)
rCEEBio(n, alpha, beta, m, lambda)
mCEEBio(x, alpha, beta, m, lambda, method="B")
```

### Arguments

`x` |
A vector of (non-negative integer) quantiles. |

`p` |
A vector of probablities. |

`n` |
The number of random values to be generated under the CEEBio distribution. |

`lambda` |
The strictly positive parameter of the binomial distribution |

`m` |
The positive parameter of the binomial distribution |

`alpha` |
The strictly positive scale parameter of the baseline exponentiated exponential distribution ( |

`beta` |
The strictly positive shape parameter of the baseline exponentiated exponential distribution ( |

`lower.tail` |
if FALSE then 1-F(x) are returned and quantiles are computed 1-p. |

`log` |
if TRUE, probabilities p are given as log(p). |

`log.p` |
if TRUE, probabilities p are given for exp(p). |

`method` |
the procedure for optimizing the log-likelihood function after setting the intial values of the parameters and data values for which the CEEBio distribution is fitted. It could be "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", or "SANN". "BFGS" is set as the default. |

### Details

These functions allow for the evaluation of the PDF, CDF, QF, random numbers and MLEs of the unknown parameters with the standard error (SE) of the estimates of the CEEBio distribution. Additionally, it offers goodness-of-fit statistics such as the AIC, BIC, -2L, A test, W test, Kolmogorov-Smirnov test, P-value, and convergence status.

### Value

dCEEBio gives the (log) probability function. pCEEBio gives the (log) distribution function. qCEEBio gives the quantile function. rCEEBio generates random values. mCEEBio gives the estimated parameters along with SE and goodness-of-fit measures.

### Author(s)

Muhammad Imran and M.H Tahir.

R implementation and documentation: Muhammad Imran imranshakoor84@yahoo.com and M.H Tahir mht@iub.edu.pk.

### References

Tahir, M. H., & Cordeiro, G. M. (2016). Compounding of distributions: a survey and new generalized classes. Journal of Statistical Distributions and Applications, 3, 1-35.

Bakouch, H. S., Ristic, M. M., Asgharzadeh, A., Esmaily, L., & Al-Zahrani, B. M. (2012). An exponentiated exponential binomial distribution with application. Statistics & Probability Letters, 82(6), 1067-1081.

Nadarajah, S. (2011). The exponentiated exponential distribution: a survey. AStA Advances in Statistical Analysis, 95, 219-251.

### See Also

### Examples

```
x<-data_guineapigs
rCEEBio(20,2,1,2,0.1)
dCEEBio(x,2,1,2,0.2)
pCEEBio(x,2,1,2,0.2)
qCEEBio(0.7,2,1,2,0.2)
mCEEBio(x,0.7,1,2,0.12, method="B")
```

*ComRiskModel*version 0.2.0 Index]