Ayana Mateus

Comparing several tests of randomness based on the difference of observations

In this work, we consider the problem of testing randomness. After reviewing several non-parametric randomness tests based on the sign of the difference of observations we shall compare their performance through a Monte Carlo simulation study.

An R implementation of several randomness tests

In many statistic methods, including distribution-free methods, we assume to work with random samples. In this note, we present randtests: an R package implementation of several nonparametric randomness tests. After a brief description of the tests included in the package, we present an application to real data sets in the field of Agricultural.

Extreme value analysis of the sea levels in Venice

The number of floods in the city of Venice has increased substantially in the last decades and can be explained by the sea level rise and land subsidence. Using Statistics of Extremes we shall model the extreme behaviour of the sea level in Venice and quantify risk through the estimation of important parameters such as return periods of high levels.

A note on the Jackson exponentiality test

In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.

Generalized least squares method in nonlinear equations

The objective of the research reported is to model the dominant height growth of eucalyptus plantations in Portugal, using the generalized least squares method. The approach used to build the model is the algebraic difference equations method. We show how it is possible to model dominant height growth using a function formulated as an algebraic difference equation with four parameters, two of them related with the stochastic part of the model, that is, related with the error structure, and the other two related with modeling the growth of the trees itself.

Estimating the Parameters of the Johnson’s SB Distribution Using an Approach of Method of Moments

In this paper, Johnson SB distribution is used to model the diameter distribution of Eucalyptus globulus in Portugal. We present a new methodology to estimate the parameters of the distribution, where we develop a system of equations that relates stand characteristics with the non‐central moments of the distribution. This way, we assure that the estimates obtained observe some restrictions which will enable them to keep a sensible biological meaning.

Empirical Power Study of the Jackson Exponentiality Test

The exponential distribution is an important model, frequently used in areas such as queueing theory, reliability and survival analysis. Therefore, the problem of testing exponentiality is an important subject in Statistics. Many tests have been proposed and in this paper we revisit the exact and asymptotic properties of the Jackson exponentiality test. Using Monte Carlo computations we study the empirical power of the Jackson test and compare it with the power of Lilliefors exponentiality test.

Exact and Approximate Probabilities for the Null Distribution of Bartels Randomness Test

In this work we revisit the statistical properties of the Bartels randomness test. The exact distribution of the statistic, under the randomization hypothesis, can only be obtained when the sample size (n) is small, since it requires the full set of permutations of the first n positive integers. Here, we present the exact null distribution without ties, for samples of size 10 ≤ n ≤ 17, extending the results available in the literature. Since the null distribution is asymptotically normally distributed, but at a slow rate, Bartels concluded that the null distribution is well approximated by a Beta distribution, for samples of size 10 ≤ n ≤ 100. We present a new approximation, based on the Edgeworth series, for the null distribution of the Bartels randomness statistic. The precision of this new approximation is also discussed.

Statistical analysis of extreme river flows

Floods are recurrent events that can have a catastrophic impact. In this work we are interested in the analysis of a data set of gauged daily flows from the Whiteadder Water river, Scotland. Using statistic techniques based on extreme value theory, we estimate several extreme value parameters, including extreme quantiles and return periods of high levels.

The difference-sign randomness test: A review

In this paper we review the properties of the difference-sign randomness test. First we analyse the exact and asymptotic distribution of the test statistic and provide a table with values for the exact distribution function, for samples of size n ≤ 32. Then, we also present several moments of the statistic test, under the null hypothesis of randomness and under the hypothesis of the existence of a linear trend. Finally, we present an illustration of the test difference-sign to a real data set.