Monthly sunspot number time series analysis and its modeling through autoregressive artificial neural network

This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p,q)). Based on minimization of AIC we find 3 and 1 as the best values of p and q respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott's index of second order and coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).Comment: 17 pages, 4 figure

Using Ranks in Parallel Line Assays

An approximation to the likelihood of a sample, based on the ranks of the observations only, is used to analyze data from a biological assay. Inferences, depending only on the ranks of the observations, are made about the potency and about the validity of assumptions made in the analysis. Inferences are made in both Bayesian and sampling theory frameworks. An example of parallel line assay is given. Copyrigh

Effect of within-sample dependence on the Mann-Whitney-Wilcoxon statistic

SUMMARY: Motivated by a problem involving correlation due to genetic relationships within a sample, we investigate the effect of within-sample dependence and between-sample independence on the variance of the Mann-Whitney-Wilcoxon statistic, given that the marginal distributions are identical in each sample. The dependence increases the variance of the statistic by a factor equal in order to the combined sample size when three specified joint marginal distributions are chosen. The results for the two-sample statistic are extended to the mean of the Kruskal-Wallis statistic, when between-sample independence and within-sample dependence are assumed. The effect is similar in this case in that the mean of the statistic is increased by a factor of the same order as the sample size. A numerical example is given

Theory and problems of advanced mathematics for engineers and scientists/ Spiegel

407 hal. : ill. ; ind. ; 24 cm

Theory and problems of advanced mathematics for engineers and scientists/ Spiegel

407 hal. : ill. ; ind. ; 24 cm

Theory and problems of advanced mathematics for engineers and scientists/ Spiegel

407 hal. : ill. ; ind. ; 24 cm

Theory and problems of advanced mathematics for engineers and scientists/ Spiegel

407 hal. : ill. ; ind. ; 24 cm