Simultaneous Joint Lower and Upper record values Probability Laws for Absolutely Continuous or Discrete Data

Gane Samb Lo; Mohammad Ahsanullah; Aladji Babacar Niang

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arXiv · 2109.04577

Simultaneous Joint Lower and Upper record values Probability Laws for Absolutely Continuous or Discrete Data

Gane Samb Lo·Mohammad Ahsanullah·Aladji Babacar Niang

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Abstract

This paper investigates the probability density function ($pdf$) of the $(2n-1)$-vector $(n\geq 1)$ of both lower and upper record values for a sequence of independent random variables with common $pdf f$ defined on the same probability space, provided that the lower and upper record times are finite up to $n$. A lot is known about the lower or the upper record values when they are studied separately. When put together, the challenges are a far bigger complicated. The rare results in the literature still present important flaws. This paper begins a new and complete investigation with a few number of records: 2 and 3. Lessons from these simple cases will allow addressing the general formulation of simultaneous joint lower-upper records.

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Gane Samb Lo, Mohammad Ahsanullah, Aladji Babacar Niang. 2021-09-09. Simultaneous Joint Lower and Upper record values Probability Laws for Absolutely Continuous or Discrete Data. https://arxiv.org/abs/2109.04577

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