S. Mane

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math.PR2023

Scaling behavior for the median of the Poisson distribution of order $k$

S. R. Mane

This note analyzes properties of the median $ν$ of the Poisson distribution of order $k$ . Given a value for the median in the interval $ν \in [1, k]$ , an equation to calculate the cor…

math.PR2023

Alternative combinatorial sum for the probability mass function of the Poisson distribution of order $k$

S. R. Mane

Kostadinova and Minkova published an expression for the probability mass function (pmf) of the Poisson distribution of order $k$ , as a combinatorial sum ($\mathit{Pliska~Stud.~Math…

math.PR2023

Convexity and monotonicity of the probability mass function of the Poisson distribution of order $k$

S. R. Mane

This note focuses on the properties of two blocks of elements of the probability mass function (pmf) of the Poisson distribution of order $k \geq 2$ . The first block is the elements f…

math.PR2023

Analytical proofs for the properties of the probability mass function of the Poisson distribution of order $k$

S. R. Mane

The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k = 1$ it is the standard Poisson distribution. Our main result is a proof that for s…

math.PR2023

Asymptotic results for the Poisson distribution of order k

S. R. Mane

The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. Its mean and variance are known, but results for its median and mode are difficult to ob…

math.PR2023

First double mode of the Poisson distribution of order $k$

S. R. Mane

The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k = 1$ it is the standard Poisson distribution. Our focus in this note is for $k \geq 2$ …

Scaling behavior for the median of the Poisson distribution of order k

Alternative combinatorial sum for the probability mass function of the Poisson distribution of order k

Convexity and monotonicity of the probability mass function of the Poisson distribution of order k

Analytical proofs for the properties of the probability mass function of the Poisson distribution of order k

Asymptotic results for the Poisson distribution of order k

First double mode of the Poisson distribution of order k

Scaling behavior for the median of the Poisson distribution of order $k$

Alternative combinatorial sum for the probability mass function of the Poisson distribution of order $k$

Convexity and monotonicity of the probability mass function of the Poisson distribution of order $k$

Analytical proofs for the properties of the probability mass function of the Poisson distribution of order $k$

First double mode of the Poisson distribution of order $k$