Consider an observable $X$ which follows some unknown statistical distribution $P$, with elements $x\in X$ in the interval $-1<x<1$.

Consider also an observable $Y$ which follows a normal distribution, with elements $y\in Y$ in the interval $-1<y<1$.

Let's say we make a sequence of observations $O$, which consist of elements $(z,p)$, such that:

• $z\in X$ with probability $p$
• $z\in Y$ with probability $1-p$

Is there a way to use Mathematica to obtain some sort of "best fit" for the probability distribution $P$ of observable $X$ from the "$Y$ contaminated" observations $O$?

For example, given the particular sequence of observations O:

https://pastebin.com/xcUdS7ch

what is a best fit for probability distribution $P$?

Consider an observable $X$ which follows some unknown statistical distribution $P$, with elements $x\in X$ in the interval $-1<x<1$.

Consider also an observable $Y$ which follows a uniform random distribution, with elements $y\in Y$ in the interval $-1<y<1$.

Let's say we make a sequence of observations $O$, which consist of elements $(z,p)$, such that:

• $z\in X$ with probability $p$
• $z\in Y$ with probability $1-p$

Is there a way to use Mathematica to obtain some sort of "best fit" for the probability distribution $P$ of observable $X$ from the "$Y$ contaminated" observations $O$?

For example, given the particular sequence of observations O:

https://pastebin.com/xcUdS7ch

what is a best fit for probability distribution $P$?