Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly establish asymptotic laws of records value, not necessarily as limits in type and their rates of convergences. Results beyond the extreme value value domain are provided. Explicit asymptotic laws concerning very usual laws and related rates of convergence are listed as well. Some of these laws are expected to be used in fitting distribution.

<div>Let $X_{1,n} \leq .... \leq X_{n,n}$ be the order statistics associated with a sample $X_{1}, ...., X_{n}$ whose pertaining distribution function (\textit{df}) is $F$. We are concerned with the functional asymptotic behaviour of the sequence of stochastic processes</div><div> </div><div>\begin{equation}<br />T_{n}(f,s)=\sum_{j=1}^{j=k}f(j)\left( \log X_{n-j+1,n}-\log<br />X_{n-j,n}\right)^{s} ,  \label{fme}<br />\end{equation}</div><div> </div><div>indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}%^{\ast}\longmapsto \mathbb{R}_{+}$ and $s \in ]0,+\infty[$ and where $k=k(n)$ satisfies</div><div> </div><div>\begin{equation*}<br />1\leq k\leq n,k/n\rightarrow 0\text{ as }n\rightarrow \infty .<br />\end{equation*}</div><div> </div><div>We show that this is a stochastic process whose margins generate estimators of the extreme value index when $F$ is in the extreme domain of attraction. We focus in this paper on its finite-dimension asymptotic law and provide a class of new estimators of the extreme value index whose performances are compared to analogous ones. The results are next particularized for one explicit class $\mathcal{F}$.</div>

In Southern Groundnut Basin of Senegal, weed management is one of the biggest challenges for improving upland rice production. This study aimed to evaluate the systematic composition and the infestation of weed species in order to promote a sustainable management in a context of biodiversity decreasing. Thus, phytosociological surveys were carried out during rainy season in upland rice fields. The results revealed that flora consisted of 62 species distributed in 47 genera and 15 families. The families with the highest species richness were Poaceae (24.2%), Fabaceae (12.9%) and Malvaceae (12.9%) which account for half of recorded species. Biological spectrum analysis showed that the flora is largely dominated by therophytes, with 95% of recorded species. Infestation diagram based on weeds abundance and frequency showed eight groups of species reflecting their degree of infestation. Among them, Digitaria horizontalis, Mariscus squarrosus, and Spermacoce stachydea belonged to major weeds and potential general weeds were potentially the most injurious against upland rice because of their high recovery and frequency. KEYWORDS Abundance Infestation Upland riceWeed

The pseudo-Lindley distribution which was introduced in Zeghdoudi and Nedjar (2016) is studied with regards to it upper tail. In that  regard, and  when the underlying distribution function follows the Pseudo-Lindley law, we investigate  the the behavior of its values, the asymptotic normality of the Hill estimator and the double-indexed generalized Hill statistic process (Ngom and Lo, 2016), the asymptotic normality of the records values and the the moment problem.

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