Chi | R Documentation |

Density, distribution function, quantile function, and random generation for the chi distribution.

```
dchi(x, df)
pchi(q, df)
qchi(p, df)
rchi(n, df)
```

`x` |
vector of (positive) quantiles. |

`q` |
vector of (positive) quantiles. |

`p` |
vector of probabilities between 0 and 1. |

`n` |
sample size. If |

`df` |
vector of (positive) degrees of freedom (> 0). Non-integer values are allowed. |

Elements of `x`

, `q`

, `p`

, or `df`

that are missing will
cause the corresponding elements of the result to be missing.

The chi distribution with `n`

degrees of freedom is the distribution of the
positive square root of a random variable having a
chi-squared distribution with `n`

degrees of freedom.

The chi density function is given by:

`f(x, \nu) = g(x^2, \nu) 2x, x > 0`

where `g(x,\nu)`

denotes the density function of a chi-square random variable
with `n`

degrees of freedom.

density (`dchi`

), probability (`pchi`

), quantile (`qchi`

), or
random sample (`rchi`

) for the chi distribution with `df`

degrees of freedom.

The chi distribution takes on positive real values. It is important because
for a sample of `n`

observations from a normal distribution,
the sample standard deviation multiplied by the square root of the degrees of
freedom `\nu`

and divided by the true standard deviation follows a chi
distribution with `\nu`

degrees of freedom. The chi distribution is also
used in computing exact prediction intervals for the next `k`

observations
from a normal distribution (see `predIntNorm`

).

Steven P. Millard (EnvStats@ProbStatInfo.com)

Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995).
*Continuous Univariate Distributions, Volume 1*.
Second Edition. John Wiley and Sons, New York.

Chisquare, Normal, `predIntNorm`

,
Probability Distributions and Random Numbers.

```
# Density of a chi distribution with 4 degrees of freedom, evaluated at 3:
dchi(3, 4)
#[1] 0.1499715
#----------
# The 95'th percentile of a chi distribution with 10 degrees of freedom:
qchi(.95, 10)
#[1] 4.278672
#----------
# The cumulative distribution function of a chi distribution with
# 5 degrees of freedom evaluated at 3:
pchi(3, 5)
#[1] 0.8909358
#----------
# A random sample of 2 numbers from a chi distribution with 7 degrees of freedom.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(20)
rchi(2, 7)
#[1] 3.271632 2.035179
```

EnvStats documentation built on Aug. 22, 2023, 5:09 p.m.

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