Calculate back from transformed data: 1.814 = -0.0432252 + 0.457229 x Ashinh ((X + 3.

[Lucky9999b]

Hi,

I was looking at the difference between sales and forecast to be able to calculate safety stock. The problem have with this article is that the difference between sales and FC is not normally distributed.
I`ve done a Johnson Transformation for Difference Sales - FC
used this std deviation to calculate needed safety stock. But now I need to transform this back. And I`m lost, since I haven`t used this type of math the last 5 years. Can someone help me and please explain how to do it:
1.814 = -0.0432252 + 0.457229 x Ashinh ((X + 3.65568) /(6.67901 )
What is X ?

Thanks!
Koen

 

[mmm4444bot]

1.814 = -0.0432252 + 0.457229 x Ashinh ((X + 3.65568) /(6.67901 )


What is X ?

I'm guessing that is the inverse hyperbolic sine function.

You have mismatched grouping symbols.

Is the following correct?

\(\displaystyle 1.814 = -0.0432252 + 0.457229 \; \cdot\)\(\displaystyle \; arcsinh\)\(\displaystyle \left(\dfrac{X + 3.65568}{6.67901}\right)\)

 

[Lucky9999b]

I'm guessing that is the inverse hyperbolic sine function.

You have mismatched grouping symbols.

Is the following correct?

\(\displaystyle 1.814 = -0.0432252 + 0.457229 \; \cdot\)\(\displaystyle \; arcsinh\)\(\displaystyle \left(\dfrac{X + 3.65568}{6.67901}\right)\)

Yes that is correct. Any idea how to solve this.
Thanks!

 

[mmm4444bot]

Use algebra, to isolate the arcsinh() term.

Then, take the hyperbolic sine of each side.

The result is a linear equation in X.

Use algebra, to solve for X. :cool:

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If your scientific calculator doesn't handle hyperbolic trig functions, here's the value for sinh(4.061914709):

29.03410266