## Abstract

The study of statistical distributions in a complex variable is one of

the most vibrant areas of research. The complex analogue of many

distributions has been studied. This article introduces the complex

analogue of Binomial distribution and Negative Binomial distribution and studies certain geometrical properties of these analogues.

It comprises the study of analytic functions defined by using the

complex versions of Binomial distribution and Negative Binomial distribution functions. It includes the problems of finding the lower

bounds of real parts of certain ratios of partial sums to the infinite

series sums for these analytic functions. Such lower bounds are determined for the said analytic functions, for their first derivatives and for

the Alexander transformation of these analytic functions.

the most vibrant areas of research. The complex analogue of many

distributions has been studied. This article introduces the complex

analogue of Binomial distribution and Negative Binomial distribution and studies certain geometrical properties of these analogues.

It comprises the study of analytic functions defined by using the

complex versions of Binomial distribution and Negative Binomial distribution functions. It includes the problems of finding the lower

bounds of real parts of certain ratios of partial sums to the infinite

series sums for these analytic functions. Such lower bounds are determined for the said analytic functions, for their first derivatives and for

the Alexander transformation of these analytic functions.

Original language | English |
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Article number | 2022.2109630 |

Pages (from-to) | 554-572 |

Number of pages | 20 |

Journal | Applied Mathematics in Science and Engineering |

Volume | 30 |

Issue number | 1 |

Publication status | Published - 9 Aug 2022 |

## Keywords

- Analytic functions
- statistical distribution
- binomial distribution
- partial sums
- ; negative binomial distributions