SMNGmoments {BayesLN} | R Documentation |

## SMNG Moments and Moment Generating Function

### Description

Functions that implement the mean, the generic moments (both raw and centered) and the moment generating function of the SMNG distribution.

### Usage

```
SMNG_MGF(
r,
mu = 0,
delta,
gamma,
lambda,
beta = 0,
inf_sum = FALSE,
rel_tol = 1e-05
)
meanSMNG(mu, delta, gamma, lambda, beta)
SMNGmoment(j, mu, delta, gamma, lambda, beta, type = "central")
```

### Arguments

`r` |
Coefficient of the MGF. Can be viewed also as the order of the logSMNG moments. |

`mu` |
Location parameter, default set to 0. |

`delta` |
Concentration parameter, must be positive. |

`gamma` |
Tail parameter, must be positive. |

`lambda` |
Shape parameter. |

`beta` |
Skewness parameter, default set to 0 (symmetric case). |

`inf_sum` |
Logical: if FALSE (default), the integral representation of the SMNG density is used, otherwise the infinite sum is employed. |

`rel_tol` |
Level of relative tolerance required for the |

`j` |
Order of the moment. |

`type` |
String that indicate the kind of moment to comupute. Could be |

### Details

If the mean (i.e. the first order raw moment) of the SMNG distribution is required, then the function `meanSMNG`

could be use.

On the other hand, to obtain the generic *j*-th moment both `"raw"`

or `"centered"`

around the mean, the function `momentSMNG`

could be used.

Finally, to evaluate the Moment Generating Function (MGF) of the SMNG distribution in the point `r`

, the function `SMNG_MGF`

is provided.
It is defined only for points that are lower then the parameter `gamma`

, and for integer values of `r`

it could also considered as the
*r*-th raw moment of the logSMNG distribution. The last function is implemented both in the integral form, which uses the routine `integrate`

,
or in the infinite sum structure.

### Examples

```
### Comparisons sample quantities vs true values
sample <- rSMNG(n=50000,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)
mean(sample)
meanSMNG(mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)
var(sample)
SMNGmoment(j = 2,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2,type = "central")
SMNGmoment(j = 2,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2,type = "raw")-
meanSMNG(mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)^2
mean(exp(sample))
SMNG_MGF(r = 1,mu = 0,delta = 2,gamma = 2,lambda = 1,beta = 2)
```

*BayesLN*version 0.2.10 Index]