Closed-Form Expressions for the Quantile Function of the Chi Square Distribution Using the Hybrid of Quantile Mechanics and Spline Interpolation

Okagbue, Hilary I.; Adamu, Muminu O.; Anake, T. A.

doi:10.1007/s11277-020-07672-w

Cited by 2 publications

(3 citation statements)

References 44 publications

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“…To demonstrate the flexibility of the quantile matching method, we have applied it to three different intervals-(1) full distribution, (2) [0.99, 0.9999999] interval, and (3) the extreme scenario [1-10 −320 , 1-10 −322 ] interval of the χ 2 distributions. Nevertheless, as the corresponding χ 2 statistics are not calculatable in [1-10 −320 , 1-10 −322 ] in RStudio, we have used the estimates obtained from quantile mechanics (QM) and natural spline interpolation for matching [45]. Furthermore, we have developed an absolute multivariate effect size method to help researchers decide between small, medium, and large effect sizes without needing to compare with other factors and facilitate the comparison of the same factor across different studies.…”

Section: Testmentioning

confidence: 99%

“…However, as the corresponding χ 2 statistics are not calculatable for quantiles larger than 1-10-320 in RStudio, direct matching is not possible. To address this issue, we have used QM and natural spline interpolation methods to obtain the estimated χ 2 statistics for those quantiles by the following steps [45]. Details are presented in Appendix B:…”

Section: The Implementation Of Quantile-matching Transformation For L...mentioning

confidence: 99%

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Identifying the Big Shots—A Quantile-Matching Way in the Big Data Context

Tam

2022

ACM Trans. Manage. Inf. Syst.

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The prevalence of big data has raised significant epistemological concerns in information systems research. This study addresses two of them—the deflated p -value problem and the role of explanation and prediction. To address the deflated p -value problem, we propose a multivariate effect size method that uses the log-likelihood ratio test. This method measures the joint effect of all variables used to operationalize one factor, thus overcoming the drawback of the traditional effect size method (θ), which can only be applied at the single variable level. However, because factors can be operationalized as different numbers of variables, direct comparison of multivariate effect size is not possible. A quantile-matching method is proposed to address this issue. This method provides consistent comparison results with the classic quantile method. But it is more flexible and can be applied to scenarios where the quantile method fails. Furthermore, an absolute multivariate effect size statistic is developed to facilitate concluding without comparison. We have tested our method using three different datasets and have found that it can effectively differentiate factors with various effect sizes. We have also compared it with prediction analysis and found consistent results: explanatorily influential factors are usually also predictively influential in a large sample scenario.

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Section: Testmentioning

confidence: 99%

Section: The Implementation Of Quantile-matching Transformation For L...mentioning

confidence: 99%

Identifying the Big Shots—A Quantile-Matching Way in the Big Data Context

Tam

2022

ACM Trans. Manage. Inf. Syst.

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“…(7) can be referred to the gamma distribution differential equation (GDDE) and the solution gives the required quantile function and can be solved using the assumed initial value conditions

. Details on the review of the method and similar methodologies can be found in [ 55 , 56 , 57 , 58 , 59 ].…”

Section: Model Formulationmentioning

confidence: 99%

Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication

Okagbue

Adamu

Anake

2020

Heliyon

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The use of quantile functions of probability distributions whose cumulative distribution is intractable is often limited in Monte Carlo simulation, modeling, and random number generation. Gamma distribution is one of such distributions, and that has placed limitations on the use of gamma distribution in modeling fading channels and systems described by the gamma distribution. This is due to the inability to find a suitable closed-form expression for the inverse cumulative distribution function, commonly known as the quantile function (QF). This paper adopted the Quantile mechanics approach to transform the probability density function of the gamma distribution to second-order nonlinear ordinary differential equations (ODEs) whose solution leads to quantile approximation. Closed-form expressions, although complex of the QF, were obtained from the solution of the ODEs for degrees of freedom from one to five. The cases where the degree of freedom is not an integer were obtained, which yielded values closed to the R software values via Monte Carlo simulation. This paper provides an alternative for simulating gamma random variables when the degree of freedom is not an integer. The results obtained are fast, computationally efficient and compare favorably with the machine (R software) values using absolute error and Kullback-Leibler divergence as performance metrics.

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Closed-Form Expressions for the Quantile Function of the Chi Square Distribution Using the Hybrid of Quantile Mechanics and Spline Interpolation

Cited by 2 publications

References 44 publications

Identifying the Big Shots—A Quantile-Matching Way in the Big Data Context

Identifying the Big Shots—A Quantile-Matching Way in the Big Data Context

Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication

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