  This paper introduces a new idea for constructing operators associated with a
certain class of probability measures. Special cases include several know
classical and noncommutative probability. The main example is derived from
Feller [30, Page 503, Example 10], i.e. the hyperbolic secant distribution. In
probability theory and statistics, the hyperbolic secant distribution is a
continuous probability distribution whose probability density function and
characteristic function are proportional to the hyperbolic secant function.
