Diametric distribution of Escheweilera ovata in a Dense Ombrophilus Forest fragment - Igarassu, Pernambuco, Brazil

 O objetivo desta pesquisa foi avaliar o comportamento de sete funções densidade de probabilidade no ajuste da distribuição diamétrica de Eschweilera ovata em um fragmento de Floresta Ombrófila Densa no estado de Pernambuco, Brasil. Os dados utilizados são provenientes dos diâmetros de 274 árvores dessa espécie medidos durante a realização de um estudo sobre a estrutura do componente arbóreo e classificação sucessional do presente fragmento. Foram testadas as seguintes funções probabilísticas: Beta, Gama, Log-Normal, Normal, SB de Johnson, Weber e Weibull 3P, utilizando intervalo de classe de 4 cm. Os resultados do teste de Kolmogorov-Smirnov indicaram que a função mais eficiente foi a Log-Normal, seguida de Weber, Weibull 3P, Beta, SB de Johnson e Gama. A distribuição Normal foi rejeitada pelo teste de Kolmogorov-Smirnov. O estudo também identificou que a distribuição em diâmetro de Escheweilera ovata nesse fragmento é do tipo decrescente.Palavras-chave: Distribuições probabilísticas; floresta nativa; “J” invertido.AbstractDiametric distribution of Escheweilera ovata in a Dense Ombrophilus Forest fragment - Igarassu, Pernambuco, Brazil. This research aimed to evaluate the behavior of seven probability density functions for fitting the diameter distribution of Escheweilera ovata in a Dense Ombrophilous Forest fragment in the State of Pernambuco, Brazil. The data used consisted of diameters of 274 trees of this species measured during a research improved to evaluate the tree components and succession classification of this fragment. The following probabilistic functions were tested: Beta, Gamma, Log-Normal, Normal, Johnson SB , Weber and Weibull 3P, it was used diametric class interval of 4 cm. The results of the Kolmogorov - Smirnov test indicated that the most efficient function was the Log-Normal, followed by Weber, Weibull 3P, Johnson SB , Beta, and Gama. The Normal distribution was rejected by the Kolmogorov - Smirnov test. This research also indicated that the Escheweilera ovata diameter distribution in this fragment is decreasingly.Keywords: Probabilistic distributions; native forest; inverted “J”.  AbstractThis research aimed to evaluate the behavior of seven probability density functions for fitting the diameter distribution of Escheweilera ovata in a Dense Ombrophilous Forest fragment in the State of Pernambuco, Brazil. The data used consisted of diameters of 274 trees of this species measured during a research improved to evaluate the tree components and succession classification of this fragment. The following probabilistic functions were tested: Beta, Gamma, Log-Normal, Normal, Johnson SB , Weber and Weibull 3P, it was used diametric class interval of 4 cm. The results of the Kolmogorov - Smirnov test indicated that the most efficient function was the Log-Normal, followed by Weber, Weibull 3P, Johnson SB , Beta, and Gama. The Normal distribution was rejected by the Kolmogorov - Smirnov test. This research also indicated that the Escheweilera ovata diameter distribution in this fragment is decreasingly.Keywords: Probabilistic distributions; native forest; inverted “J”. 

Reliability growth modeling analysis of the space shuttle main engines based upon the Weibull process

The Weibull process, identified as the inhomogeneous Poisson process with the Weibull intensity function, is used to model the reliability growth assessment of the space shuttle main engine test and flight failure data. Additional tables of percentage-point probabilities for several different values of the confidence coefficient have been generated for setting (1-alpha)100-percent two sided confidence interval estimates on the mean time between failures. The tabled data pertain to two cases: (1) time-terminated testing, and (2) failure-terminated testing. The critical values of the three test statistics, namely Cramer-von Mises, Kolmogorov-Smirnov, and chi-square, were calculated and tabled for use in the goodness of fit tests for the engine reliability data. Numerical results are presented for five different groupings of the engine data that reflect the actual response to the failures

Harbin: a quantitation PCR analysis tool

Objectives: To enable analysis and comparisons of different relative quantitation experiments, a web-browser application called Harbin was created that uses a quantile-based scoring system for the comparison of samples at different time points and between experiments. Results: Harbin uses the standard curve method for relative quantitation to calculate concentration ratios (CRs). To evaluate if different datasets can be combined the Harbin quantile bootstrap test is proposed. This test is more sensitive in detecting distributional differences between data sets than the Kolmogorov–Smirnov test. The utility of the test is demonstrated in a comparison of three grapevine leafroll associated virus 3 (GLRaV-3) RT-qPCR data sets. Conclusions: The quantile-based scoring system of CRs will enable the monitoring of virus titre or gene expression over different time points and be useful in other genomic applications where the combining of data sets are required

Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems

The Weibull distribution is a commonly used model for the strength of brittle materials and earthquake return intervals. Deviations from Weibull scaling, however, have been observed in earthquake return intervals and in the fracture strength of quasi-brittle materials. We investigate weakest-link scaling in finite-size systems and deviations of empirical return interval distributions from the Weibull distribution function. We use the ansatz that the survival probability function of a system with complex interactions among its units can be expressed as the product of the survival probability functions for an ensemble of representative volume elements (RVEs). We show that if the system comprises a finite number of RVEs, it obeys the $\kappa$-Weibull distribution. We conduct statistical analysis of experimental data and simulations that show good agreement with the $\kappa$-Weibull distribution. We show the following: (1) The weakest-link theory for finite-size systems involves the $\kappa$-Weibull distribution. (2) The power-law decline of the $\kappa$-Weibull upper tail can explain deviations from the Weibull scaling observed in return interval data. (3) The hazard rate function of the $\kappa$-Weibull distribution decreases linearly after a waiting time $\tau_c \propto n^{1/m}$, where $m$ is the Weibull modulus and $n$ is the system size in terms of representative volume elements. (4) The $\kappa$-Weibull provides competitive fits to the return interval distributions of seismic data and of avalanches in a fiber bundle model. In conclusion, using theoretical and statistical analysis of real and simulated data, we show that the $\kappa$-Weibull distribution is a useful model for extreme-event return intervals in finite-size systems.Comment: 33 pages, 11 figure

Statistical tests for whether a given set of independent, identically distributed draws does not come from a specified probability density

We discuss several tests for whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly Kuiper's variant, which focus on discrepancies between the cumulative distribution function for the specified probability density and the empirical cumulative distribution function for the given set of i.i.d. draws. Unfortunately, variations in the probability density function often get smoothed over in the cumulative distribution function, making it difficult to detect discrepancies in regions where the probability density is small in comparison with its values in surrounding regions. We discuss tests without this deficiency, complementing the classical methods. The tests of the present paper are based on the plain fact that it is unlikely to draw a random number whose probability is small, provided that the draw is taken from the same distribution used in calculating the probability (thus, if we draw a random number whose probability is small, then we can be confident that we did not draw the number from the same distribution used in calculating the probability).Comment: 18 pages, 5 figures, 6 table