Title: An alternative to continuous univariate distributions supported on a bounded interval: The BMT distribution,
Abstract: In this paper, we introduce the BMT distribution as an unimodal alternative
to continuous univariate distributions supported on a bounded interval. The
ideas behind the mathematical formulation of this new distribution come from
computer aid geometric design, specifically from Bezier curves. First, we
review general properties of a distribution given by parametric equations and
extend the definition of a Bezier distribution. Then, after proposing the BMT
cumulative distribution function, we derive its probability density function
and a closed-form expression for quantile function, median, interquartile
range, mode, and moments. The domain change from [0,1] to [c,d] is mentioned.
Estimation of parameters is approached by the methods of maximum likelihood and
maximum product of spacing. We test the numerical estimation procedures using
some simulated data. Usefulness and flexibility of the new distribution are
illustrated in three real data sets. The BMT distribution has a significant
potential to estimate domain parameters and to model data outside the scope of
the beta or similar distributions.