View source: R/family.aunivariate.R

betaR | R Documentation |

Estimation of the shape parameters of the two-parameter beta distribution.

```
betaR(lshape1 = "loglink", lshape2 = "loglink",
i1 = NULL, i2 = NULL, trim = 0.05,
A = 0, B = 1, parallel = FALSE, zero = NULL)
```

`lshape1, lshape2, i1, i2` |
Details at |

`trim` |
An argument which is fed into |

`A, B` |
Lower and upper limits of the distribution.
The defaults correspond to the |

`parallel, zero` |
See |

The two-parameter beta distribution is given by
`f(y) =`

```
(y-A)^{shape1-1} \times
(B-y)^{shape2-1} / [Beta(shape1,shape2)
\times (B-A)^{shape1+shape2-1}]
```

for `A < y < B`

, and `Beta(.,.)`

is the beta function
(see `beta`

).
The shape parameters are positive, and
here, the limits `A`

and `B`

are known.
The mean of `Y`

is ```
E(Y) = A + (B-A) \times shape1 /
(shape1 + shape2)
```

, and these are the fitted values of the object.

For the standard beta distribution the variance of `Y`

is
```
shape1 \times
shape2 / [(1+shape1+shape2) \times (shape1+shape2)^2]
```

.
If `\sigma^2= 1 / (1+shape1+shape2)`

then the variance of `Y`

can be written
`\sigma^2 \mu (1-\mu)`

where
`\mu=shape1 / (shape1 + shape2)`

is the mean of `Y`

.

Another parameterization of the beta distribution involving the mean
and a precision parameter is implemented in `betaff`

.

An object of class `"vglmff"`

(see `vglmff-class`

).
The object is used by modelling functions
such as `vglm`

,
`rrvglm`

and `vgam`

.

The response must have values in the interval (`A`

,
`B`

). VGAM 0.7-4 and prior called this function
`betaff`

.

Thomas W. Yee

Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1995).
Chapter 25 of:
*Continuous Univariate Distributions*,
2nd edition, Volume 2, New York: Wiley.

Gupta, A. K. and Nadarajah, S. (2004).
*Handbook of Beta Distribution and Its Applications*,
New York: Marcel Dekker.

`betaff`

,
`Beta`

,
`genbetaII`

,
`betaII`

,
`betabinomialff`

,
`betageometric`

,
`betaprime`

,
`rbetageom`

,
`rbetanorm`

,
`kumar`

,
`simulate.vlm`

.

```
bdata <- data.frame(y = rbeta(1000, shape1 = exp(0), shape2 = exp(1)))
fit <- vglm(y ~ 1, betaR(lshape1 = "identitylink",
lshape2 = "identitylink"), bdata, trace = TRUE, crit = "coef")
fit <- vglm(y ~ 1, betaR, data = bdata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit) # Useful for intercept-only models
bdata <- transform(bdata, Y = 5 + 8 * y) # From 5 to 13, not 0 to 1
fit <- vglm(Y ~ 1, betaR(A = 5, B = 13), data = bdata, trace = TRUE)
Coef(fit)
c(meanY = with(bdata, mean(Y)), head(fitted(fit),2))
```

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