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

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