A Note on the Possible Misuse of the Kolmogorov-Smirnov Test

Crutcher, Harold L.

doi:10.1175/1520-0450(1975)014<1600:anotpm>2.0.co;2

Cited by 90 publications

(61 citation statements)

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“…Because the samples being tested in this work are the same samples being used in deriving the distributions parameters, the KS test is also known as the lilliefors test. The KS/lilliefors value (here after referred just as KS) for rejection/ acceptance of H 0 will depend on the sample size being used to test the parametric distribution, on the shape of the parametric distribution and, of course, on the significance level chosen by the user (Crutcher, 1975). The confidence in accepting or rejecting the theoretical distributions was measured by the p-value (p).…”

Section: Methodsmentioning

confidence: 99%

Standardized precipitation index based on pearson type III distribution

Blain

2011

Rev. bras. meteorol.

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The initial step in calculating the Standardized Precipitation Index (SPI) is to determine a probability density function (pdf) that describes the precipitation series under analysis. Once this pdf is determined, the cumulative probability of an observed precipitation amount is computed. The inverse normal function is then applied to the cumulative probability. The result is the SPI. This article assessed the changes in SPI final values, when computed based on Gamma 2-parameters (Gam) and Pearson Type III (PE3) distributions (SPIGam and SPIPE3, respectively). Monthly rainfall series, available from five weather stations of the State of São Paulo, were chosen for this study. Considering quantitative and qualitative assessments of goodness-of-fit (evaluated at 1-, 3-, and 6-months precipitation totals), the PE3 distribution seems to be a better choice than the Gam distribution, in describing the longterm rainfall series of the State of São Paulo. In addition, it was observed that the number of SPI time series that could be seen as normally distributed was higher when this drought index was computed from the PE3 distribution. Thus, the use of the Pearson type III distribution within the calculation algorithm of the SPI is recommended in the State of São Paulo. Keywords: drought, Gamma distribution, SPI RESUMO: ÍNDICE PADRONIZADO DE PRECIPITAÇÃO BASEADO NA DISTRIBUIÇÃO PEARSON TIPO III O cálculo do Índice Padronizado de Precipitação (IPP) inicia-se com a adoção de uma distribuição paramétrica (dp) utilizada para a estimativa das probabilidades de ocorrência associadas a uma série de precipitação pluvial. Após essa escolha, a probabilidade acumulada de ocorrência de um determinado valor de precipitação é calculada. O IPP é obtido após a aplicação da função normal inversa a essa probabilidade acumulada. O artigo avaliou as alterações nos valores finais do IPP, quando calculado com base nas distribuições Gama com dois parâmetros (Gam) e Pearson tipo III (PE3; IPPGam e IPPPE3, respectivamente). Utilizaram-se dados de precipitação pluvial de cinco localidades do Estado de São Paulo, nas escalas de 1, 3 e 6 meses. Aplicando testes de aderência, tanto qualitativos, quanto quantitativos, verificou-se que as probabilidades associadas às séries utilizadas foram melhores estimadas por meio da PE3. Foi também observado, que o número de séries temporais do IPP que podem ser consideradas normalmente distribuídas, foi maior quando este índice de seca foi calculado com base na PE3. Dessa forma, recomenda-se a adoção da PE3 no cálculo do IPP no Estado de São Paulo. Palavras-Chave: seca, distribuição gama, IPP

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Section: Methodsmentioning

confidence: 99%

Standardized precipitation index based on pearson type III distribution

Blain

2011

Rev. bras. meteorol.

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“…The false positive rate from the K-S appears to be conservative (i.e., less than 0.05). This might be because if parameters are estimated from the sample to provide a control distribution against which the sample is to be tested, the actual significance level of rejection is smaller that the selected significance level (Crutcher, 1975).…”

Section: Results and Commentsmentioning

confidence: 99%

A comparison of inverse transform and composition methods of data simulation from the Lindley distribution

Okwuokenye

Peace

2016

CSAM

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“…In fact, as evidenced by a previous study [88], the SPI is an index with several univariate probability distribution recommendations that typically rely on the Kolmogorov-Smirnov test. However, this test has been shown to be relatively insensitive in previous statistical analyses [89] and requires time-consuming Monte Carlo simulation of critical values when applied to distributions derived from the data [90,91]. Moreover, probability distribution fitting for the SPI is also complicated by the presence of periods with zero precipitation, as has been previously described [92], and current procedures do not adequately capture the likelihood of zero precipitation events.…”

Section: Standardized Precipitation Indexmentioning

confidence: 99%

An Analysis of the Occurrence Probabilities of Wet and Dry Periods through a Stochastic Monthly Rainfall Model

Caloiero

Sirangelo

Coscarelli

et al. 2016

Water

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Stochastic simulators can effectively generate the intrinsic variability of the rainfall process, which is an important issue in the analysis of the projections uncertainties. In this paper, a procedure for stochastic modeling of precipitation at monthly scale is proposed. The model adopts variable transformations, which are finalized to the deseasonalization and the Gaussianization of the monthly rainfall process, and includes a procedure for testing the autocorrelation. The model was applied to a homogeneous database of monthly rainfall values registered in 12 rain gauges in the region of Calabria (Southern Italy). After the estimation of the model parameters, a set of 10 4 years of monthly rainfall for each rain gauge was generated by means of a Monte Carlo technique. Then, dry and wet periods were analyzed through the application of the standardized precipitation index (SPI). Some results, confirmed through the application of the drought severity index (DSI), showed that the proposed model provided a good representation of the monthly rainfall for the considered rain gauges. Moreover, the results of the SPI application indicate a greater probability of dry conditions than wet conditions, especially when long-term precipitation patterns are considered.

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A Note on the Possible Misuse of the Kolmogorov-Smirnov Test

Cited by 90 publications

References 0 publications

Standardized precipitation index based on pearson type III distribution

Standardized precipitation index based on pearson type III distribution

A comparison of inverse transform and composition methods of data simulation from the Lindley distribution

An Analysis of the Occurrence Probabilities of Wet and Dry Periods through a Stochastic Monthly Rainfall Model

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