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We propose a scheme for estimating a nonlinear functional of a three-dimensional random variable's probability density. The analyzed random variables' blur coefficients of kernel functions are shown as the result of undetermined parameter and mean-square deviations of the analyzed random variables. The considered functional for a family of unimodal distribution policies is based on the probability density rather than the density characteristics and is not dependent on the density coefficients. The estimated approximation errors for the nonlinear function of the probability density are estimated using the values of the newly introduced generalized parameter for a family of three-dimensional log-normal distribution laws of independent random variables. We investigate the possibility of utilizing the suggested method for estimating nonlinear functionals of probability densities that differ from log-normal distribution rules. The effect of the resulting approximation errors on the root-mean-square criteria for reconstructing a nonparametric estimation of a three-dimensional random variable is investigated.

Source link: https://ui.adsabs.harvard.edu/abs/2022OIDP...58..188L/abstract

This paper conducted a fatigue reliability analysis on a braced monopod structure located in Madura North Java Sea to find the most reliable fatigue measurement of each structure's components by examining the effect of some load random variable. Running fatigue analysis using only one-year wave data for 59-year SEAFINE wave data is found by running fatigue testing using only one-year wave counts for 59-year SEAFINE wave data. Analysis will be divided by a safety factor and service life to reveal annual fatigue losses. The result of reliability analysis is little affected by the S-N curve parameter, according to many performance metrics. As load random variable, fatigue reliability analysis would only include annual fatigue loss and local and global stress analysis as part of the load random variable.

Source link: https://ui.adsabs.harvard.edu/abs/2022E&ES.1065a2026P/abstract

The sums of random variables is one of the most important statistics in statistics and probability theory, but one of the most important statistics is random variables. This paper presented the probability density function for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Rani, Pranav, and Ram Awadh. In addition, the Lindley components' failure time has investigated the availability and the mean time to failure of a 1 out of a n cold standby spare system.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220808006Y/abstract

Let X_1, X_2,2̆2ef be a sequence of i. d random variables that are not expected to be observed in sequence. The random sets R_k(k=1,2,2̆2ef) are unconserved with common distribution, according to the Ignatov's Theorem. We conclude this paper with some possible link to scan results.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220806791L/abstract

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