On absolute central moments of Poisson distribution

On Non Asymptotic Expansion of the MME in the Case of Poisson Observations

The problem of parameter estimation by observations of inhomogeneous Poisson processes is considered. The method of moments estimator is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the expansion of the moments of this estimator and the expansion of the distribution function. The stochastic expansion, expansion of the moments and the expansion of distribution function are non asymptotic in nature. Several examples are considered.

Sharp and Simple Bounds for the raw Moments of the Binomial and Poisson Distributions

We prove the inequality $E[(X/μ)^k] \le (\frac{k/μ}{\log(k/μ+1)})^k \le \exp(k^2/(2μ))$ for sub-Poissonian random variables, such as Binomially or Poisson distributed random variables with mean $μ$. The asymptotics $1+O(k^2/μ)$ can be shown to be tight for small $k$. This improves over previous uniform bounds for the raw moments of those distributions by a factor exponential in $k$.

Beta Poisson-G Family of Distributions: Its Properties and Application with Failure Time Data

A new generalization of the family of Poisson-G is called beta Poisson-G family of distribution. Useful expansions of the probability density function and the cumulative distribution function of the proposed family are derived and seen as infinite mixtures of the Poisson-G distribution. Moment generating function, power moments, entropy, quantile function, skewness and kurtosis are investigated. Numerical computation of moments, skewness, kurtosis and entropy are tabulated for select parameter values. Furthermore, estimation by methods of maximum likelihood is discussed. A simulation study is …

幂指数泊松分布的再认识

The exponentiated exponential Poisson distribution revisited

通过给出三参数指数Poisson概率分布${\rm EEP}(α, β, λ)$的特征函数$ϕ_ξ(t)$和矩母函数$M_ξ(t)$的显式封闭形式表达式，刻画和研究了三参数指数Poisson概率分布${\rm EEP}(α, β, λ)$，并证明了已有的正整数阶矩$\mathbb Eξ^ν, ν\in \mathbb N$的级数和积分形式表达式对所有$ν>1-α, α>0$都是有效的.

重尾分布的分数阶绝对矩

Fractional absolute moments of heavy tailed distributions

给出了几种计算分数阶绝对矩的简便方法，并将其应用于重尾分布。我们使用分数阶微分技术，得到$E[|X-μ|^γ]$与$1<γ<2$和$μ\in\mathbb{R}$的公式。重点讨论了重尾分布，并给出了几个例子，给出了分数阶绝对矩的解析表达式。作为应用，我们计算了预测和参数估计问题的分数阶矩误差。

A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework

The absolute-moment method is widespread for estimating the Hurst exponent of a fractional Brownian motion $X$. But this method is biased when applied to a stationary version of $X$, in particular an inverse Lamperti transform of $X$, with a linear time contraction of parameter $θ$. We present an adaptation of the absolute-moment method to this framework and we compare it to the maximum likelihood method, with simulations and an application to a financial time series. While it appears that the maximum-likelihood method is more accurate than the adapted absolute-moment estimation, this last met…

正态分布的矩和绝对矩

Moments and Absolute Moments of the Normal Distribution

我们提出了正态分布的（原始和中心）矩和绝对矩的公式。我们注意到，这些结果并不新鲜，但许多教科书至少遗漏了其中的一些。因此，我们认为这些公式及其推导在这些笔记中是值得收集的。

关于 variance-gamma 分布的矩

On the moments of the variance-gamma distribution

本文推导 variance-gamma 分布矩及绝对矩的新闭式公式，并据此给出两个相关零均值正态随机变量乘积对应矩的新表达式。

实阶矩、尾部表示与对数均值

Tail representations for absolute, signed-power, inverse, and logarithmic moments

本文建立任意随机变量实阶矩的统一框架，通过累积分布函数和生存函数给出积分表示，涵盖连续、离散和混合分布，并应用于zeta和Skellam分布，同时得到对数矩表示，连接对数均值、拉普拉斯变换与Frullani恒等式。