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右删失寿命数据的经验似然AI 解读

When the empirical likelihood (EL) of a parameter θ is constructed with right censored data, literature shows that − 2log (empirical likelihood ratio) typically has an asymptotic scaled chi-squared distribution, where the scale parameter is a function of some unknown asymptotic variances. Therefore, the EL construction of confidence intervals for θ requires an additional estimation of the scale parameter. Additional estimation would reduce the coverage accuracy for θ. By…

存在观测死时间时的泊松强度估计AI 解读

Phase Doppler interferometry (PDI) is a nonintrusive technique frequently used to obtain information about spray characteristics. Understanding spray characteristics is of critical importance in many areas of science, including liquid fuel spray combustion, spray coatings, fire suppression, and pesticides. PDI measures the size and velocity of individual droplets in a spray. Due to the design of the instrument, recordings of the PDI contain gaps, called dead times. The…

随机截断模型中截断概率的估计AI 解读

Under random truncation, a pair of independent random variables $X$ and $Y$ is observable only if $X$ is larger than $Y$. The resulting model is the conditional probability distribution $H( x, y) =P[X \leq x,Y \leq y|X \geq Y]$. For the truncation probability $\alpha=P[X \geq Y]$, a proper estimate is not the sample proportion but $\alpha_n=\int G_n (s)dF_n(s)$ where $F_n$ and $G_n$ are product limit estimates of the distribution functions $F$ and$G$ of $X$ and$Y$,…

随机截断下的强大数定律AI 解读

The random truncation model is defined by the conditional probability distribution $H (x, y) =P[X\leq x,Y\leq y |X \geq Y] where $X$ and $Y$ are independent random variables. A problem of interest is the estimation of the distribution function $F$ of $X$ with data from the distribution $H$. Under random truncation, $F$ need not be fully identifiable from $H$ and only a part of it, say $F_0$ , is. We show that the nonparametric MLE $F_n$ of $F_0$ obeys the strong law of large numbers in the sense that for any nonnegative, measurable function $…