Hi everyone

I am trying to fit a nonlinear function to many simulated data sets all with the same basic structure. I've little experience with nonlinear models though, so would appreciate some advice. The function I need must meet the criteria below, and what I am most interested in is the value of Y at X=0.

Model characteristics should be as follows. (Will also attach a graphic of possible examples)

1. I'm predicting Y (continuous variable) from a single continuous predictor (X).

2. All X values are greater than or equal to 0

3. All Y values are proportions, so constrained between 0 and 1.

4. Where X=0, Y is NOT constrained to a value of Y=0, in fact this would be very unlikely in my data.

5. The slope of the function is greatest at X=0 and declines monotonically to 0 as X increases and Y approaches 1.

Thanks for any suggestions