# 70_moment-based_statistics: Moment-Based Statistics In probhat: Multivariate Generalized Kernel Smoothing and Related Statistical Methods

## Description

Compute moment-based statistics from probability distributions.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```ph.mean (sf, ..., n.intervals=200) ph.sd (sf, ..., n.intervals=200) ph.var (sf, ..., n.intervals=200) ph.skewness (sf, ..., n.intervals=200) ph.kurtosis (sf, ..., n.intervals=200) moment (sf, nth, ..., n.intervals=200) central.moment (sf, nth, ..., n.intervals=200) standardized.moment (sf, nth, ..., n.intervals=200) raw.moment (sf, nth, about=0, ..., n.intervals=200) ```

## Arguments

 `sf` A suitable function object. Here, this is a univariate PMF or spline-based CDF. Refer to the references and see also sections. `nth` Integer, the nth moment

.

 `about` Numeric, the about constant for raw moments. `n.intervals` Integer. In the discrete case, ignored. In the continuous case, the number of intervals, used in the numerical approximation. `...` Ignored.

## Details

The mean/sd/var/skewness/kurtosis functions all call the moment function.

If the moment function is called with nth equal zero, it returns one.
If called with nth=1 (the mean), it computes the the first raw moment.
If called with nth=2 (the variance), it computes the second central moment.
If called with nth=3 (the skewness), it computes the third standardized moment.
If called with nth=4 (the kurtosis), it computes the fourth standardized moment.
And if called with nth>4, it also computes the nth standardized moment.

Note that currently, the standard deviation, variance and higher moments, should should not be regarded as accurate.

## Value

A single numeric value.

## References

Refer to the vignette for an overview, references and better examples.

Succinct Constructors
Discrete Kernel Smoothing, Continuous Kernel Smoothing, Empirical-Like Distributions

probmv, rng

quartiles, ntiles, ph.median, ph.quantile
ph.mode, ph.modes

## Examples

 ```1 2 3 4 5 6 7 8``` ```prep.ph.data () cFh <- cdfuv.cks (height) ph.mean (cFh) ph.sd (cFh) ph.skewness (cFh) ph.kurtosis (cFh) ```

probhat documentation built on May 12, 2021, 5:08 p.m.