Wrapped exponential distribution

In probability theory and directional statistics, a wrapped exponential distribution is a wrapped probability distribution that results from the "wrapping" of the exponential distribution around the unit circle. == Definition == The probability density function of the wrapped exponential distribution is f WE ( θ ; λ ) = ∑ k = 0 ∞ λ e − λ ( θ + 2 π k ) = λ e − λ θ 1 − e − 2 π λ , {\displaystyle f_{\text{WE}}(\theta ;\lambda )=\sum _{k=0}^{\infty }\lambda e^{-\lambda (\theta +2\pi k)}={\frac {\lambda e^{-\lambda \theta }}{1-e^{-2\pi \lambda }}},} for 0 ≤ θ < 2 π {\displaystyle 0\leq \theta <2\pi } where λ > 0 {\displaystyle \lambda >0} is the rate parameter of the unwrapped distribution.

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