View source: R/univariate.mle.R

MLE of distributions defined for proportions | R Documentation |

MLE of distributions defined for proportions.

```
kumar.mle(x, tol = 1e-07, maxiters = 50)
simplex.mle(x, tol = 1e-07)
zil.mle(x)
unitweibull.mle(x, tol = 1e-07, maxiters = 100)
cbern.mle(x, tol = 1e-6)
sp.mle(x)
```

`x` |
A vector with proportions or percentages. Zeros are allowed only for the zero inflated logistirc normal distribution (zil.mle). |

`tol` |
The tolerance level up to which the maximisation stops. |

`maxiters` |
The maximum number of iterations the Newton-Raphson will perform. |

The distributions included are the Kumaraswamy, zero inflated logistic normal, simplex, unit Weibull and continuous Bernoulli and standard power. Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson algorithm which is faster. See wikipedia for the equations to be solved.

Usually a list with three elements, but this is not for all cases.

`iters` |
The number of iterations required for the Newton-Raphson to converge. |

`param` |
The two parameters (shape and scale) of the Kumaraswamy distribution. For the zero inflated logistic normal, the probability of non zeros, the mean and the unbiased variance. |

`loglik` |
The value of the maximised log-likelihood. |

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

Kumaraswamy P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology 46(1-2): 79-88.

Jones M.C. (2009). Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6(1): 70-81.

Mazucheli J., Menezes A.F.B., Fernandes L.B., de Oliveira R.P. and Ghitany M.E. (2020). The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics, DOI:10.1080/02664763.2019.1657813

Leemis L.M. and McQueston J.T. (2008). Univariate Distribution Relationships. The American Statistician, 62(1): 45-53.

You can also check the relevant wikipedia pages.

```
zigamma.mle, censweibull.mle
```

```
u <- runif(1000)
a <- 0.4 ; b <- 1
x <- ( 1 - (1 - u)^(1/b) )^(1/a)
kumar.mle(x)
```

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