Weighted multimodal family of distributions with sine and cosine weight functions
In this paper, the moment of various types of sine and cosine functions are derived for any random variable. For an arbitrary even probability density function, the sine and cosine moments are used to define new families of univariate multimodal probability density and their corresponding characteri...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-08-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844020316005 |
| _version_ | 1817982226056347648 |
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| author | Ayman Alzaatreh Jaber Kazempoor Adel Ahmadi Nadi |
| author_facet | Ayman Alzaatreh Jaber Kazempoor Adel Ahmadi Nadi |
| author_sort | Ayman Alzaatreh |
| collection | DOAJ |
| description | In this paper, the moment of various types of sine and cosine functions are derived for any random variable. For an arbitrary even probability density function, the sine and cosine moments are used to define new families of univariate multimodal probability density and their corresponding characteristic functions. For illustration, two weighted multimodal generalizations of the t distribution are investigated. Furthermore, a method of calculating some interesting improper integrals is also presented. Finally, an explicit expression of the probability density function of the sum of independent t-distributed random variables with odd degrees of freedom is derived. |
| first_indexed | 2024-04-13T23:17:58Z |
| format | Article |
| id | doaj.art-f068420075454e61a89cf853a1c1f037 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-13T23:17:58Z |
| publishDate | 2020-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-f068420075454e61a89cf853a1c1f0372022-12-22T02:25:21ZengElsevierHeliyon2405-84402020-08-0168e04757Weighted multimodal family of distributions with sine and cosine weight functionsAyman Alzaatreh0Jaber Kazempoor1Adel Ahmadi Nadi2Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates; Corresponding author.Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Islamic Republic of IranDepartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Islamic Republic of IranIn this paper, the moment of various types of sine and cosine functions are derived for any random variable. For an arbitrary even probability density function, the sine and cosine moments are used to define new families of univariate multimodal probability density and their corresponding characteristic functions. For illustration, two weighted multimodal generalizations of the t distribution are investigated. Furthermore, a method of calculating some interesting improper integrals is also presented. Finally, an explicit expression of the probability density function of the sum of independent t-distributed random variables with odd degrees of freedom is derived.http://www.sciencedirect.com/science/article/pii/S2405844020316005MathematicsMomentsCharacteristic functionEven probability density functionParseval's identity |
| spellingShingle | Ayman Alzaatreh Jaber Kazempoor Adel Ahmadi Nadi Weighted multimodal family of distributions with sine and cosine weight functions Heliyon Mathematics Moments Characteristic function Even probability density function Parseval's identity |
| title | Weighted multimodal family of distributions with sine and cosine weight functions |
| title_full | Weighted multimodal family of distributions with sine and cosine weight functions |
| title_fullStr | Weighted multimodal family of distributions with sine and cosine weight functions |
| title_full_unstemmed | Weighted multimodal family of distributions with sine and cosine weight functions |
| title_short | Weighted multimodal family of distributions with sine and cosine weight functions |
| title_sort | weighted multimodal family of distributions with sine and cosine weight functions |
| topic | Mathematics Moments Characteristic function Even probability density function Parseval's identity |
| url | http://www.sciencedirect.com/science/article/pii/S2405844020316005 |
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