For the future development of a financial series, I have been given expected returns, volatility, and two percentiles (25th and 75th).
Without the two percentiles given, I would choose to model the above with the lognormal distribution (ie, $\ln(1+r)$ is normally distributed).
However, this generally won't give me a perfect calibration given the percentiles.
Is there a standard/well-known/classical/reasonable alternative (with a strictly positive pdf for all values larger than 0) to the lognormal distribution that also allows for fitting (to) these percentiles?