Sentence examples for maxima and partial from inspiring English sources

In statistical context, we are very concerned with the ASCLT in the joint version for the maxima and partial sums.

The goal of this note is to investigate the general pattern of the ASCLT for the maxima and partial sums of i.i.d.i.d

In addition, the almost sure central limit theorem in the joint version for log-average of maxima and partial sums of independent and identically distributed random variables was obtained by Peng et al. [9], whereas the joint version of the almost sure limit theorem for log-average of maxima and partial sums of stationary Gaussian random variables was derived by Dudziński [10].

The central Arctic is one of three sea regions with recurrent winter maxima and partial summer ice cover, and Figure 4 shows the trend in yearly averages for the central Arctic, with the anomalous low cover years (1990, 2007) apparent.

The almost sure central limit theorem in the joint version for log average in the case of independent and identically distributed random variables is obtained by Peng et al. [9]; a joint version of almost sure limit theorem for log average of maxima and partial sums in the case of stationary Gaussian random variables is derived by Dudziński [10].

The almost sure central limit theorem in a joint version for log average in the case of independent and identically distributed random variables was obtained by Peng et al. [9], a joint version of almost sure limit theorem for log average of maxima and partial sums in the case of stationary Gaussian random variables was derived by Dudziński [10].

Further, Peng et al. [17 19], Zhao et al. [20], and Tan and Wang [21] studied the maximum and partial sums of a standardized nonstationary Gaussian sequence.

Zhao et al. [20] obtained the following almost sure limit theorem for maximum and partial sums of standardized nonstationary Gaussian sequence.

We will study and establish the ASCLT for maximum (M_{n}) and maximum and partial sums of the standardized Gaussian sequences, and we will show that the ASCLT holds under a fairly general growth condition on (d_{k}=k^{-1}exp(ln^{alpha}k)), (0leqalpha<1/2).

The universal results in almost sure central limit theorems for the maxima (M_{n}) and partial sums and maxima ((S_{n}/sigma_{n}, M_{n})) are established, respectively, where (S_{n}=sum_{i=1}^{n}X_{i}), (sigma^{2}_{n}=operatorname{Var}S_{n}), and (M_{n}=max_{1leq ileq n}X_{i}).

Dudziński [13, 14] proved the almost sure limit theorems in the joint version for the maxima and the partial sums of stationary Gaussian sequences, that is, let be stationary Gaussian sequences and,,, for all (1.4).