Description Usage Arguments Details Value Warning Author(s) References See Also Examples

Density, distribution function, quantile function and random generation for Mandel's k statistic, a measure of relative precision compared to a common variance.

1 2 3 4 |

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`g` |
number of groups for which k is calculated. |

`n` |
number of observations in each group of data for which k is calculated. |

`B` |
Number of observations. If 'length(B) > 1', the length is taken to be the number required. |

`lower.tail` |
logical; if TRUE (default), probabilities are P[X <= x]; otherwise, P[X > x]. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

Mandel's k for one of a set of *g* standard deviations *s* is calculated as

*k=\frac{s_{ij}^2}{∑_{i=1}^p{s_{ij}^2/p}}*

Since the numerator is chi-squared(n-1), or Gamma((n-1)/2, 2), and the denominator
can be written as the sum of the same quantity and a pooled variance with distribution
Gamma((g-1)*(n-1)/2, 2), k is distributed as Beta((n-1)/2, (g-1)(n-1)/2).
Quantiles, probabilities, density and random numbers can therefore be generated
from the Beta distribution. For example, qmandelk is calculated as
`sqrt( g * qbeta( (n-1)/2, (g-1)*(n-1)/2))`

.

dmandelh returns the density at `x`

, pmandelh the cumulative probability,
qmandelh the quantiles for probability `p`

and rmandelh returns `B`

random values drawn from the distribution.

Vector values of x, p, q and g are permitted, in which case the functions return vectors.

Note that `rmandelk`

uses `B`

and not `n`

(as do most R random
number functions) for number of random draws; this is because `n`

is conventionally
used for the number of replicates per group. Be careful when using named parameters!

S. L. R. Ellison, s.ellison@lgc.co.uk

None.

1 2 3 4 5 6 7 |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.