aka25 wrote:
>
> Hi there,
>
> If I have a statistics distribution, and I have the information of what the y
> value is when x = 0 (at the center of the distribution), and know what the y
> value is when the concavity of the graph changes at x = +SD (standard
> deviation), and then know that the y value as x approaches infinity is 0 and
> my data looks like so:
Micah: A distribution need not have a point of inflection (though it
must under certain real-world-plausible smoothness conditions.) If it
does, it need not be at 1SD from the mean; that is a property that the
normal distribution happens to have. Knowing this, are you sure you
still want to proceed? If so:
In general, the data you give (density at center, density at one
standard deviation) are overdetermined for a normal distribution
(where their ratio is always e:1) but underdetermined for a general
symmetric function. Choose yourself a three-parameter family of
symmetric distributions - typically (mean, SD, heaviness of tail) and
you can probably find a solution within that.
You can also probably do something similar for data of the form
(density at center, density at point of inflection) if that is really
what you want to do. Note that the point of inflection, like all
locations of specific derivative values, is numerically poorly
conditioned - that is, it is not accurately inferred from even slightly
noisy data!
-Robert Dawson
.
.
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