In statistic, when we want to find the estimation of the model parameters, do we only work with the density function?
Why do we need to work with density function instead of Cumulative distribution function?
Also, sometimes we need to work with cumulative distribution function. For example, if we need to transform the margins to be uniform margins we can use cumulative distribution function, or sometimes the empirical cumulative distribution function.
Why we do not use density in transformation and use it in estimation?
What are the benefits of density function over the Cumulative distribution function and ecdf and vice verse?