Regional Climate Models in the Simulation of the Drought of the 1970’s and 1980’s Years in Senegal (In West Africa)

West Africa was hit by an unprecedented drought in the 1970’s and 1980’s years, with dramatic consequences for surface and groundwater resources. In the context of climate change, there are many studies for the prediction of the increase in the occurrence of these droughts. To predict this situation in the Senegalese region, it is necessary to use regional climate models, which carrying out the study. This work deals with the interest to examine the capacity of the RCMs (regional climate models) in order to reproduce the deficit on the 1970’s year rainfall in Senegal. In this work, we used daily precipitation data from five (5) regional climate models to characterize the droughts in Senegal by using the SPI (Standardized Precipitation Index) on different time scales (3, 6, 12 and 24 months). For this purpose, the index was calculated over two distinct periods: 1951-1969 and 1970-1990. The results show that the period 1970-1990 was drier than the period 1951-1969. For the zonal average, the results show that the North of Senegal was more affected by this deficit rainfall than the South part. The analysis of the interannual variability of rainfall for some stations in Senegal shows that the drought did not start at the same time throughout the zone.

Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

On the Functional Empirical Process and Its Application to the Mutual Influence of the Theil-Like Inequality Measure and the Growth

We set in this paper a coherent theory based on functional empirical processes that allows to consider both the poverty and the inequality indices in one Gaussian field in which the study of the influence of the one over the other is done. We use the General Poverty Index (GPI), that is a class of poverty indices gathering the most common ones and a functional class of inequality measures including the Entropy Measure, the Mean Logarithmic Deviation, the different inequality measures of Atkinson, Champernowne, Kolm and Theil called Theil-Like Inequality Measures (TLIM). Our results are given in a unified approach with respect to the two classes instead of their particular elements. We provide the asymptotic laws of the variations of each class over two given periods and the ratio of the variation and derive confidence intervals for them. Although the variances may seem somehow complicated, we provide R codes for their computations and apply the results for the pseudo-panel data for Senegalwith a simple analysis.

Functional Kernel Estimation of the Conditional Extreme Quantile under Random Right Censoring

The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many investigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a heavy-tailed distribution is discussed when some functional random covariate (i.e. valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided.

High Moments Jarque-Bera Tests for Arbitrary Distribution Functions

The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The tests use as many moments as possible whereas the JB classical test is supposed to test only skewness and kurtosis for normal variates. But our results unveil the relations between the coeffients in the JB classical test and the moments, showing that it really depends on the first eight moments. This is a new explanation for the powerfulness of such tests. General Chi-square tests for an arbitrary model, not only normal, are also derived. We make use of the modern functional empirical processes approach that makes it easier to handle statistics based on the high moments and allows the generalization of the JB test both in the number of involved moments and in the underlying distribution. Simulation studies are provided and comparison cases with the Kolmogorov-Smirnov’s tests and the classical JB test are given.

Functional Weak Laws for the Weighted Mean Losses or Gains and Applications

In this paper, we show that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are gathered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions w and d. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison among statistics in terms of dependence and mutual influence. The results are particularized for usual statistics like the Kakwani and Shorrocks ones that are mainly used in welfare analysis. Data-driven applications based on pseudo-panel data are provided.

Trend and Return Level Analysis of Extreme Rainfalls in Senegal

In recent years, Senegal has been confronted with increasingly frequent and damaging extreme events. In the context of climate change, we conducted this study to characterize the trends of rainfall extremes in Senegal. In this work, we used daily rainfall data from 27 stations in Senegal from the period 1951 to 2005 (55 years). To study their linear trends, non-stationary extreme value models with time as a covariate are fitted to evaluate them. Our results indicate a decreasing trend of extreme rainfalls at most of the stations except for 5 stations. However, the decreasing trends are only significant for two stations (Thiès and Kidira), however, this can only be taken as information that climate change may have already impacted extreme rainfalls. For the 20-year and 30-year return periods, the results show that they have undergone changes, in fact for almost all stations, the trends in return periods are decreasing.

Probabilistic, Statistical and Algorithmic Aspects of the Similarity of Texts and Application to Gospels Comparison

The fundamental problem of similarity studies, in the frame of data-mining, is to examine and detect similar items in articles, papers, and books with huge sizes. In this paper, we are interested in the probabilistic, and the statistical and the algorithmic aspects in studies of texts. We will be using the approach of k-shinglings, a k-shingling being defined as a sequence of k consecutive characters that are extracted from a text (k ≥ 1). The main stake in this field is to find accurate and quick algorithms to compute the similarity in short times. This will be achieved in using approximation methods. The first approximation method is statistical and, is based on the theorem of Glivenko-Cantelli. The second is the banding technique. And the third concerns a modification of the algorithm proposed by Rajaraman et al. ([1]), denoted here as (RUM). The Jaccard index is the one being used in this paper. We finally illustrate these results of the paper on the four Gospels. The results are very conclusive.

Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator

In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.

Functional Diversity of Mycorrhizal Fungi Has Differential Effects on Salinity Tolerance of <i>Acacia seyal</i>(Del.) Seedlings

Acacia seyal is a leguminous plant that plays an important role in the ecosystem of Sahelian zone by producing gum, wood and fodder. The growth of A. seyal is subject to many constraints as salinity which can affect the development of this tree. Therefore, soil microorganisms can help A. seyal to better tolerate the effects of negative environmental stresses. The contribution of arbuscular mycorrhizal fungi (AMF) to the salt tolerance of A. seyal, was evaluated by testing the effects of eight different arbuscular mycorrhizal fungi (AMF) isolates in the performance of A. seyal seedlings subjected to different levels of salinity (0, 340 and 680 mM). The results based on growth parameters of shoot and root parts, shoot mineral N, P, K and Na content as well as survival rates and mycorrhization showed that AMF improved mineral nutrition of A. seyal seedlings during salt stress. The combination between AMF and salinity provided evidence that the efficiency of AMF isolates were variable in improving mineral nutrition and mortality rate for A. seyal seedlings related to the level of salt stress. However, the effects of inoculation were variable depending to the AMF isolate associated with seedlings and the level of salinity, suggesting that interactions between plants and AMF can be modulated by both AMF diversity and the type and level of abiotic factors. Rhizophagus intraradices was more efficient at 680 mM NaCl in plant growth and mineral uptake while Glomus deserticola did not promote a better plant development than most of the other species inoculated to seedlings.