How Do I Model Data That Follows an Exponential Distribution

[DamarC]

Hello,

I am looking to model data that appears to follow the exponential distribution with a mean of 1.8, as indicated by the screenshots from the CAPABILITY procedure.

Exponential Distribution PDF fittingExponential Distribution CDF fitting

Knowing this, how would one go on about trying to build a predictive model for this data? I narrowed down the number of variables to use with the Rapid Predictive Modeler (I do not have Enterprise Miner installed on my computer) and I have tried using the MODEL procedure to do a non-linear modeling of the data but the fit is very poor with an r-square of 0.0674 and a root MSE of 1.8 (to give perspective, the mean of the data is 1.8). Any advice on this topic would be greatly appreciated!

PROC MODEL DATA=stdize_data;
	PARAMETERS 	w_1 0
				w_2 0
				w_3 0
				w_4 0
			  	lambda 1;
	BOUNDS 	w_1 >= 0,
			w_2 >= 0,
			w_3 >= 0,
			w_4 >= 0,
		  	lambda > 0;
	RESTRICT 	w_1 + w_2 + w_3 + w_4 = 1;
	CER = lambda * exp(-lambda * (w_1*x_1 + w_2*x_2 + w_3*x_3 + w_4*x_4));
	FIT CER / MAXITER=10000 OUT=model_results OUTALL;
RUN;

[Reeza]

https://blogs.sas.com/content/iml/2015/09/16/plot-distrib-exp.html

[Rick_SAS]

I guess I don't understand what you mean by "how do I build a predictive model."  If there are no covariates, then the expected value of your model is 1.8 and the model 

Y = 1.8 

is the linear model that fits the data.

In your PROC MODEL statement, you have X1-X4, which appear to be explanatory variables. But if these are covariates, then you should not have used PROC CAPABILITY to fit the response, you should have used a regression procedure such as PROC GENMOD.

Please explain whether this is a univariate model or a regression problem. If regression, please describe the data.