cumulative distribution function vs probability density function

[Luciano Nitsch]

Hi everyone,

According to my lecture slides you can compute the Marginal Effects for continuous X for the probit model using this formula:

B1*ϕ(B0+B1X)
So for example if the question is: "How much does the predicted value of Y change if X changes from 0.1 to 0.2?"
Which value do I have to use for my X: 0.1 or 0.2? Intuitively i'd say 0.2 but I am not sure.
My tutor also says that there is a difference between the cumulative distribution function and the probability density function. But which is the difference?

I know this is more about Stata and not general statistic questions but I didn't know where else to ask and maybe you could help me.

Thank you very much in advance,

Luciano

[FernandoRios]

neither
the marginal effect is for a marginal change: dp(y|x)/dx
however, if you are interested in the average effect of a change like the one you describe you need:
dp(y|x) = mfx(x) * dx
change in the probability = marginal effect * the change in x.
so in your case the DX=0.2 - 0.1 = 0.1

for your second question, you need to revise your math and statistics background. (specifically what is a distribution function, derivatives and integrals).
HTH