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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.

Instances of the Meijer G function may be used as representations for the probability density function (p.d.f.) and cumulative density function (c.d.f.) of several distributions. However, although the Meijer G function is a very handy representation for the p.d.f. and c.d.f. of these distributions, and nevertheless prominent progress has been made in its computation, this still remains very heavy, and time consuming, even with the newer versions of symbolic and extended precision softwares, so that the development of sharp and fast approximations is a desirable goal. In this paper it is shown how extremely sharp approximations for particular instances of the Meijer G function may be based on the probability density and cumulative distribution functions of the Generalized Near-Integer Gamma distribution.

The sphericity and equivariance-equicorrelation tests are two important tests in Multivariate Analysis used, for example, to test assumptions on the structure of covariance matrices which are required in different areas of statistics, for instance in Analysis of Variance and Principal Component Analysis. In this work we combine both tests in a single test, assuming, for the covariance matrix, in the null hypothesis a sphericity structure and in the alternative hypothesis an equivariance-equicorrelation structure. We derive the likelihood ratio test statistic, the expression of its h-th null moment and the expression of the characteristic function of its logarithm, and we show that the exact distribution of the likelihood ratio test statistic is the same as the distribution of the product of independent Beta random variables. Asymptotic approximations are developed in terms of mixtures of Gamma distributions, and numerical studies to assess their quality are developed.

In this paper we show that, when the coefficients are not all positive, the distribution of the linear combination of independent Gamma random variables may be represented in form of an infinite mixture of differences of two independent Gamma random variables. Based on truncations of this mixture two precise approximations are developed. Numerical computational studies are conducted to access the quality of these approximations.

In this paper the authors combine the equicorrelation and equivariance test introduced by Wilks [13] with the likelihood ratio test (l.r.t.) for independence of groups of variables to obtain the l.r.t. of block equicorrelation and equivariance. This test or its single block version may find applications in many areas as in psychology, education, medicine, genetics and they are important “in many tests of multivariate analysis, e.g. in MANOVA, Profile Analysis, Growth Curve analysis, etc” [12, 9]. By decomposing the overall hypothesis into the hypotheses of independence of groups of variables and the hypothesis of equicorrelation and equivariance we are able to obtain the expressions for the overall l.r.t. statistic and its moments. From these we obtain a suitable factorization of the characteristic function (c.f.) of the logarithm of the l.r.t. statistic, which enables us to develop highly manageable and precise near-exact distributions for the test statistic.

The equicorrelation and equivariance test, also known as compound symmetry, or intraclass correlation test, was introduced in [9] and is of great importance in different fields in multivariate statistics like in Analysis of Variance, Profile Analysis and Growth Curve analysis. In this paper we consider an extension of this test based on the composition of three tests; the equality of covariance matrices test, the independence of several groups of variables test and the equicorrelation and equivariance test. Our objective is to derive a procedure that allows us to test whether in different populations we have equal covariance matrices all with a block-diagonal equicorrelation and equivariance structure, i.e. a block-diagonal matrix where each diagonal block has an equicorrelation and equivariance structure. We designate this test by the multisample block-diagonal equicorrelation and equivariance test. Taking this test as the composition of the three tests mentioned above we show that it is possible to obtain the likelihood ratio test statistic, the expression of its null moments and the characteristic function of its logarithm. This approach also allows us to write the characteristic function of the logarithm of likelihood ratio test statistic in a way that enables the development of new and highly accurate near-exact distributions for that statistic. These distributions have been applied with considerable success to various test statistics used in multivariate analysis. Furthermore they are easy to implement computationally and will allow us to carry out the test with a high precision.

The multi-sample block-scalar sphericity test represents a wide family of tests since it has as particular cases several well known and fundamental tests in multivariate statistics, like for example the test of independence of several groups of variables, the sphericity test and the test of equality of several variance-covariance matrices. In this work we address the case where we have several independent samples extracted from complex multivariate Normal populations and we want to test if the covariance matrices are equal for all populations and if for each population they have a particular diagonal structure. We show that by decomposing the null hypothesis into three partial null hypotheses it is possible to easily derive the likelihood ratio test statistic, the expression of its h-th moment and the characteristic function of its logarithm. Using this method we are able to better analyze the structure of the exact distribution and, using the induced factorization on the characteristic function, we show how it is possible to develop simple but highly accurate near-exact distributions for the likelihood ratio test statistic.

The authors show how working on the characteristic function of the negative logarithm of the likelihood ratio test statistic to test that in a multivariate normal model the means in the mean vector are all equal and the covariance matrix is circular, it is possible to obtain its exact distribution in a closed finite form. This distribution is a Generalized Integer Gamma distribution.

The multi-sample independence test for several groups of variables is a generalization of the usual independence test which is of great importance in several areas of application. The exact distribution of the likelihood ratio test statistic of this test, both in the real or complex multivariate Normal setting, has a non-manageable and complicated expression. Using a novel approach, we develop near-exact distributions for the distribution of the test statistic which are highly accurate and easy to use. These are obtained decomposing the null hypothesis of the test into two null hypotheses, one to test the equality of the several variance-covariance matrices and the other to test, assuming that the first null hypothesis is not rejected, the independence of several groups of variables. This procedure allows us to obtain, in a simple way, the likelihood ratio test statistic, the expression of its h-th null moment and the characteristic function of its logarithm. The decomposition of the null hypothesis induces a factorization of the characteristic function of the logarithm of the test statistic which enables the development of near-exact distributions. The near-exact distributions obtained have the form of mixtures of Generalized Near-Integer Gamma distributions revealing a hight degree of precision in the approximation and good asymptotic properties for the different parameters involved.

At CERN, a non caesiated H− ion volume source derived from the DESY ion source is being commissioned. For a proposed High Power Superconducting Proton Linac (HP‐SPL), a non caesiated plasma generator was designed to operate at the two orders of magnitude larger duty factor required by the SPL. The commissioning of the plasma generator test stand and the plasma generator prototype are completed and briefly described. The 2 MHz RF generators (100 kW, 50 Hz repetition rate) was successfully commissioned; its frequency and power will be controlled by arbitrary function generators during the 1 ms plasma pulse. In order to characterize the plasma, RF‐coupling, optical spectrometer, rest gas analyzer and Langmuir probe measurements will be used. Optical spectrometry allows direct comparison with the currently commissioned Linac4 H− ion source plasma. The first measurements of the optical emission of the Linac4 ion source and of the SPL plasma generator plasmas are presented.

The multi‐sample block‐matrix sphericity test and its particular cases have wide applications in several areas. However, the practical implementation of this test has been hindered by difficulties in handling the exact distribution of the associated statistic and the non‐availability in the literature of asymptotic distributions. We use a decomposition of the null hypothesis into three null hypotheses to obtain very well‐fit and highly manageable near‐exact distributions for the likelihood ratio test statistic of this test and its particular cases. These distributions will allow for the easy computation of well‐fit near‐exact quantiles and p‐values.

In the LINAC4 H− source and the SPL plasma generator at CERN, the plasma is heated by a 100 kW, 2 MHz RF system. Matching of the load impedance to the final amplifier is achieved with a resonant network. The system implements a servo loop for power stabilization and frequency hopping to cope with the detuning effects induced by the plasma. This paper provides a detailed description of the system, including the pulse rate increase to 50 Hz for use in the SPL plasma generator. The performances, measurements of RF power coupling, contribution of the plasma to the impedance as well as first operation are reported.

Using a suitable decomposition of the null hypothesis of the test of sphericity for k blocks of pi variables, into a sequence of conditionally independent null hypotheses we show that it is possible to obtain the expression of the likelihood ratio test statistic, the expression for the h‐th null moment and the characteristic function of the logarithm of the likelihood ratio test statistic. The exact distribution of the logarithm of the likelihood ratio test statistic is then obtained as the distribution of the sum of a Generalized Integer Gamma random variable (r.v.) with the sum of a number of independent Logbeta r.v.’s. This distribution takes the form of a single Generalized Integer Gamma distribution when each set of variables has two variables. In the general case, the development of near‐exact distributions arises, from the previous decomposition of the null hypothesis and the consequent induced factorization on the characteristic function, as a natural and practical way to approximate the exact dis...

This paper presents the experimental status of charmonium spectroscopy and describes the technique of cc formation in pp annihilations used by the experiment E760 at Fermilab. Results from 1990 data taking are reported.