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4af6d330-66a2-4b46-ac51-064b578f95b7 87 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

If this is slightly increased to 13.25, we get α > 1, and no error

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X 30.4 0 63.9 387.1 330 187.3 495.9 18 163.3 128.8 101 mat :

3 appVersion 0.99.7251

278.7

13.22

X.mean X Mean : 180.47

x# LNX 0 x# 0 ≡ x# ln cases :

X ln vectorize Mean #

LNX X LNX vectorize :

LNX.mean LNX Mean : 4.3613

A X.mean ln LNX.mean - : 0.8343

α 14 A * / 114 A * 3 / + sqrt + (* eval : 0.7352

Works correct only if numerically evaluated.

Otherwise gives different results in evaluating F & G when using the vectorize operater ( only if α ≥ 1 )

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ε 1012 -^:

β X.mean α / eval : 245.4756

α 0.7352

If 0 < α < 1 in Eqn 1 throwss an error . This behaviour seems to be a bug, either

in SS 7251 OR evaluation of Eqn 1. But it evaluates correctly in EXCEL

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z F 1 β α^α Gamma * / x α 1 -^x β / - exp * x ε z int eval * :

Eqn 1

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u Q j 1 u rows range B j el u j el F : eval 11 line for B 21 line :

x α 1 -^x β / - exp * x 0 X 2 el Int 1 β α^α Gamma * / * #

G X Q : #

X F vectorize #

X 1 el F 1.29

lastError x - not defined.

lastError x - not defined.

As per Jean's method

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ε 11012 -^*

This solves the problem

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eval(,) drops timing ~ 0.75
acc acuuracy 50/100 plentty. z α β CDF 1 α Gamma β α^* / x α 1 -^e x β / -^* x ε z int eval * :

z α β CDF2 0 z 0 ≡ 1 α Gamma β α^* / x α 1 -^e x β / -^* x ε z int eval * cases :

Mathcad result

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Excel Result

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X α β CDF vectorize #

X 30.4 0 63.9 387.1 330 187.3 495.9 18 163.3 128.8 101 mat

X α β CDF2 vectorize 1.29 0 2.6078 14.4668 12.421 7.2425 18.3415 0.7866 6.3574 5.0736 101 mat

X 2 el 0

X 1 el 30.4

LNX 3.414443 0 4.157319 5.958683 5.799093 5.232712 6.206374 2.890372 5.095589 4.858261 101 mat

X.mean 180.47

X 1 el α β CDF 1.29

LNX.mean 4.3613

X 2 el α β CDF2 0

A 0.83428

α 0.7352

α 0.7352

β 245.4756

β 245.4756

ε 1012 -^:

1 α Gamma β α^* / x α 1 -^x β / - exp * x ε X 1 el int eval * 1.29

ε 11012 -^*

u F3 0 u 0 ≡ 1 α Gamma β α^* / x α 1 -^x β / - exp * x ε u int eval * cases :

X 1 el F3 1.29

Excel Result

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u α β CDF3 j 1 u rows range : u j el 0 ≡ B j el 0 : B j el u j el F3 : eval if B 31 line :

α 0.7352

β 245.4756

Wrong Result

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Wrong results X α β CDF3 1.2925 0 2.6131 14.4981 12.4477 7.2577 18.3811 0.788 6.3705 5.0841 101 mat

Python 3.8.3 Result

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Data X 30.4 0 63.9 387.1 330 187.3 495.9 18 163.3 128.8 101 mat