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

This implements the Fortran algorithm AS 99 by Hill et al.

1 | ```
FitJohnsonDistribution(XBAR, SD, RB1, BB2)
``` |

`XBAR` |
mean |

`SD` |
standard deviation |

`RB1` |
coefficient of skewness |

`BB2` |
coefficient of kurtosis or a negative value to indicate the lognormal family |

Vector of length 6 with named elements: "ITYPE", "GAMMA", "DELTA", "XLAM", "XI", "IFAULT". ITYPE is 1, SL; 2 for SU, 3 for SB, 4 for Normal. GAMMA, DELTA, XLAM, XI are the parameters for the Johnson distribution, where for the SL family, XI=-1. IFAULT is an error indicator, 0 means no error, 1 if the input standard deviation is negative, 2 if the kurotis, BB2, is less than skewness coefficient plus 1 and 3 if SB-fitting failed to converge and an SL or ST was fit instead.

A. I. McLeod

D. Hill, R. Hill, and R. L. Holder, Algorithm AS 99. Fitting Johnson curves by moments, Appl. Statist.,25, No. 2, 180-189 (1976).

I. D. Hill, Algorithm AS 100. Normal-Johnson and Johnson-normal transformations, Appl. Statist.,25, No. 2, 190-192 (1976).

`yJohnsonDistribution`

,
`zJohnsonDistribution`

1 2 | ```
#fit SL with mean 1, variance 1 and skewness 2.
FitJohnsonDistribution(1, 1, 2, -1)
``` |

```
ITYPE GAMMA DELTA XLAM XI IFAULT
1.0000000 -0.6626648 1.8136194 1.0000000 -0.6776508 0.0000000
```

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