Inverse distribution

Inverse distribution refers to the mathematical function that calculates the value of the input variable that corresponds to a given probability or percentile in a probability distribution. In the case of continuous distributions such as the Normal and Gamma distributions, the inverse distribution function does not have a simple functional form, but approximations have been developed due to the significance of these models.From: Simulation Methodology for Statisticians, Operations Analysts, and Engineers [2017]

Random Variable Generation

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Published in Zaven A. Karian, Edward J. Dudewicz, Modern Statistical, Systems, and GPSS Simulation, 2020

Zaven A. Karian, Edward J. Dudewicz

Suppose that we have selected a distribution function FX(·) for the random variable of interest and now wish to generate independent random variables X1, X2,… each of which has this distribution function. If FX(·) is a continuous and increasing function then it has an inverse function, often called the inverse distribution function, or percentile function, denoted by FX−1(⋅).

Reliability-based first-ply failure envelopes of composite tubes subjected to combined axial and torsional loadings

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Published in Mechanics Based Design of Structures and Machines, 2023

Rajamohan Ganesan, Ajeesh Suresh Nair

The adequate number of simulations required for the reliability study of the composite tubes is thus established as 400. The magnitudes of the first-ply failure loadings corresponding to different values of reliability are calculated using the Inverse Distribution Function which is the inverse of the Cumulative Distribution Function (CDF). From a set of values (in the present case a set of 400 values of each first-ply failure loading), the Inverse Distribution Function returns the value of the first-ply failure loading corresponding to a particular reliability value. The first-ply failure loadings corresponding to different reliability values are obtained using MATLAB®. The probabilistic distributions of the first-ply failure loadings of the composite tubes fit well with the Gaussian distribution.

Inverse distribution

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Random Variable Generation

Reliability-based first-ply failure envelopes of composite tubes subjected to combined axial and torsional loadings