# PCE - Why is coefficient of variance and standard deviation so high?

I am using the PCE methodology. There are three input variables. Two inputs are defined as having a gaussian distribution and the third variable is defined as having a uniform distribution. The coefficient of variance and standard deviation are unreasonably high, as in 700%… why?

Dear @Pilgrim

Best regards
Styfen

Dear Styfen,
Thank you for the response I appreciate it. I am using the PCE method to approximate the ignition delay time (tau). The equation is as follows:
tau = Aphiexp(E/(R*T))
A is defined as having a Gaussian distribution [0.00112 0.0017]
phi = constant
E is defined as having a Gaussian distribution [28.0 3.96]
R = constant
T is defined as having a uniform distribution [1243 1276]
Note: the temperature was measured as 1243 K with an uncertainty of 2.66%, hence the defined bounds for the uniform distribution.

Background: ignition delay time was measured at 17 different temperatures, the ignition delay time measurements were plotted against temperature, a curve fit was applied to the data in order to calculate A and E.

Pilgrim

Correction:
bounds for uniform distribution of T are [1210 1276]

Dear Pilgrim,
just a quick comment on my side: according to your post, your model is

with \phi constant, and \exp(...) being a positive quantity. However, according to your post you are using a Gaussian A with mean 1.12\cdot 10^{-3} and standard deviation 1.7\cdot 10^{-3}, hence a large coefficient of variation there of approx 1.5.
Now, the Gaussian distribution is symmetric around the mean, which means that more than 1/4 of the values of A will be negative. This means that regardless on the distribution of the exponential part of your equation, \tau will have a lot of negative values, and therefore a relatively low mean. At the same time, it will also have a very large variance due to the change of sign. This may easily explain your observed large coefficient of variation.
From a quick numerical investigation (I don’t have either \phi nor R), it looks like R affects strongly the variance of the model. E.g. with \phi = 1, R = 30, I get a CoV of 700%, while with \phi=1, R=50 the CoV goes down to 1.5.