Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication
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 distributio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-11-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844020323665 |
| _version_ | 1819315503331540992 |
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| author | Hilary Okagbue Muminu O. Adamu Timothy A. Anake |
| author_facet | Hilary Okagbue Muminu O. Adamu Timothy A. Anake |
| author_sort | Hilary Okagbue |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-24T10:01:08Z |
| format | Article |
| id | doaj.art-1e3ce57697b54e5c8f61ac1400691373 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-12-24T10:01:08Z |
| publishDate | 2020-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-1e3ce57697b54e5c8f61ac14006913732022-12-21T17:01:02ZengElsevierHeliyon2405-84402020-11-01611e05523Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communicationHilary Okagbue0Muminu O. Adamu1Timothy A. Anake2Department of Mathematics, Covenant University, Ota, Nigeria; Corresponding author.Department of Mathematics, University of Lagos, Akoka, Lagos, NigeriaDepartment of Mathematics, Covenant University, Ota, NigeriaThe 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.http://www.sciencedirect.com/science/article/pii/S2405844020323665Electrical engineeringSafety engineeringStatisticsRisk analysisQuantile functionInverse cumulative distribution function |
| spellingShingle | Hilary Okagbue Muminu O. Adamu Timothy A. Anake Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication Heliyon Electrical engineering Safety engineering Statistics Risk analysis Quantile function Inverse cumulative distribution function |
| title | Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication |
| title_full | Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication |
| title_fullStr | Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication |
| title_full_unstemmed | Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication |
| title_short | Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication |
| title_sort | approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication |
| topic | Electrical engineering Safety engineering Statistics Risk analysis Quantile function Inverse cumulative distribution function |
| url | http://www.sciencedirect.com/science/article/pii/S2405844020323665 |
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