Functions and CALL Routines |

Returns the noncentrality parameter from a chi-square distribution.

Category: | Mathematical |

Syntax | |

Arguments | |

Details | |

Examples |

## Syntax |

CNONCT(x,df,prob) |

Details |

The CNONCT function returns the nonnegative noncentrality parameter from a noncentral chi-square distribution whose parameters are x, df, and nc. If prob is greater than the probability from the central chi-square distribution with the parameters x and df, a root to this problem does not exist. In this case a missing value is returned. A Newton-type algorithm is used to find a nonnegative root nc of the equation

where

where is the probability from the gamma distribution given by

If the algorithm fails to converge to a fixed point, a missing value is returned.

Examples |

data work; x=2; df=4; do nc=1 to 3 by .5; prob=probchi(x,df,nc); ncc=cnonct(x,df,prob); output; end; run; proc print; run;

Computations of the Noncentrality Parameters from the Chi-squared Distribution

OBS x df nc prob ncc 1 2 4 1.0 0.18611 1.0 2 2 4 1.5 0.15592 1.5 3 2 4 2.0 0.13048 2.0 4 2 4 2.5 0.10907 2.5 5 2 4 3.0 0.09109 3.0

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