I am fitting a model's parameters to grouped data by maximizing the likelihood equation:
$L(\theta)=N!\prod_{i=1}^{G}\frac{p_i(\theta)^{n_i}}{n_i!}$
$\theta$ is the vector of parameters. $n_i$ is the number of observations in group i. That is, $n_i=x_i-x_{i-1}$ where $x_i$ is an individual observation. $N$ is the total number of observations ($N=\sum_{i}n_i$). $G$ is the number of groups.
And $p_i(\theta)=F(x_i;\theta)-F(x_{i-1};\theta)$, where $F(x_i;\theta)$ is the distribution function I am trying to fit to the data.
My problem is that the observations are normalized (they are percentiles). So $0