Normal_sym_trunc_ab {ExtDist} | R Documentation |

## The symmetric truncated normal distribution.

### Description

Density, distribution, quantile, random number
generation and parameter estimation functions for the symmetric truncated normal distribution with parameters, `sigma`

,
`a`

and `b`

which represent the lower and upper truncation points respectively.
Parameter estimation can be based on a weighted or unweighted i.i.d sample and can be carried out numerically.

### Usage

```
dNormal_sym_trunc_ab(
x,
sigma = 0.3,
a = 0,
b = 1,
params = list(sigma, a, b),
...
)
pNormal_sym_trunc_ab(
q,
sigma = 0.3,
a = 0,
b = 1,
params = list(mu = 2, sigma = 5, a = 0, b = 1),
...
)
qNormal_sym_trunc_ab(
p,
sigma = 0.3,
a = 0,
b = 1,
params = list(mu = 2, sigma = 5, a = 0, b = 1),
...
)
rNormal_sym_trunc_ab(
n,
mu = 2,
sigma = 3,
a = 0,
b = 1,
params = list(sigma, a, b),
...
)
eNormal_sym_trunc_ab(X, w, method = "numerical.MLE", ...)
lNormal_sym_trunc_ab(
X,
w,
mu = 2,
sigma = 3,
a = 0,
b = 1,
params = list(sigma, a, b),
logL = TRUE,
...
)
```

### Arguments

`x` , `q` |
A vector of quantiles. |

`a` , `b` |
Boundary parameters. |

`params` |
A list that includes all named parameters. |

`...` |
Additional parameters |

`p` |
A vector of probabilities. |

`n` |
Number of observations. |

`mu` , `sigma` |
Shape parameters. |

`X` |
Sample observations. |

`w` |
An optional vector of sample weights. |

`method` |
Parameter estimation method. |

`logL` |
logical;if TRUE, lNormal_sym_trunc_ab gives the log-likelihood, otherwise the likelihood is given. |

### Details

The normal symmetric truncated distribution is a special case of the trucated normal distribution.
See `Normal_trunc_ab`

.

### Value

dNormal_sym_trunc_ab gives the density, pNormal_sym_trunc_ab the distribution function, qNormal_sym_trunc_ab the quantile function, rNormal_sym_trunc_ab generates random deviates,and eNormal_sym_trunc_ab estimates the parameters. lNormal_sym_trunc_ab provides the log-likelihood function.

### Author(s)

Haizhen Wu and A. Jonathan R. Godfrey.

### See Also

ExtDist for other standard distributions.

*ExtDist*version 0.7-2 Index]