Ussian. These analyses could be conducted by the lognormal continuous probability distribution. However, some features such as the slant contain negative ACY 241 web values which are not useful for lognormal. Therefore, in order to build a unique framework, a GEV distribution is proposed which has been traditionally used for modeling extremes of natural phenomena such as waves, winds, temperatures, earthquakes, floods, etc. We try to generalize the human signature variability response through a unique distribution model we use to smooth the fit according to our collected data histogram. The GEV probability density distribution has the following prescription:+1hist(l),1 x? t ?e ?s where t ??8????< 1 ?x x ?=xs??if x 6?0 if x ?:??e x ?swith x bounded by +/ from above if > 0 and from below if < 0. The symbols , and represent the location, scale and shape distribution parameters. The shape value determines the family of the extreme value representation from Fisher Tippett Types I, II, III which correspond to = 0, < 0 and > 0 separately. Also the shape value is directly related to Gumbel, Fr het and Weibull families according to extreme value theory. Some of the studied parameters share common information, independently of the database analyzed. The statistical similarity of the probability density distribution of one parameter for one database comparing with the others is also analyzed. Such statistical similarity analysis is performed through two-sample Kolmogorov-Smirnov test (KS) [47?9]. This method allows us to cluster some single features from a database. For graphical representation only, we have clustered the results when the feature is statistically similar between the databases. This non-parametric test evaluates the degree of similarity between two probability density functions. The null hypothesis H0 of the test means that two data distributions are from the same distribution. The alternative hypotheses H1 means that two data distributions are different. In our implementation, the significance level chosen is 5 . To accept the null hypothesis, the asymptotic p-value is calculated, which should be as near to 1 as possible. Such a p-value represents the probability that the null hypothesis is true by observing the extreme test under the null hypothesis. After estimating the feature distribution parameters, the mean, variance, skewness and ICG-001 cost kurtosis values of the distribution are provided for better knowledge of the feature distribution. The mean, variance and skewness indicate the symmetry of the distribution, and the kurtosis the peakedness of the distribution. The mean square difference between the parametric and non-parametric estimation is also given.ResultsThousands of features can be obtained from a signature to model its lexical morphology. In this section the lexical morphological features considered most relevant, i.e. descriptive and common, are described alongside their estimated PDFs. They are presented in a top-downPLOS ONE | DOI:10.1371/journal.pone.0123254 April 10,7 /Modeling the Lexical Morphology of Western Handwritten Signaturesprocess, starting from global feature characterization and finishing with specific details in the signature.Signature envelopeThe envelope of the signature is a fictitious shape which encloses each deposited signature. Each signature has its own specific envelope. In this study we have analyzed the average envelope of the signatures per databases by using the Active Shape Model (ASM). This me.Ussian. These analyses could be conducted by the lognormal continuous probability distribution. However, some features such as the slant contain negative values which are not useful for lognormal. Therefore, in order to build a unique framework, a GEV distribution is proposed which has been traditionally used for modeling extremes of natural phenomena such as waves, winds, temperatures, earthquakes, floods, etc. We try to generalize the human signature variability response through a unique distribution model we use to smooth the fit according to our collected data histogram. The GEV probability density distribution has the following prescription:+1hist(l),1 x? t ?e ?s where t ??8????< 1 ?x x ?=xs??if x 6?0 if x ?:??e x ?swith x bounded by +/ from above if > 0 and from below if < 0. The symbols , and represent the location, scale and shape distribution parameters. The shape value determines the family of the extreme value representation from Fisher Tippett Types I, II, III which correspond to = 0, < 0 and > 0 separately. Also the shape value is directly related to Gumbel, Fr het and Weibull families according to extreme value theory. Some of the studied parameters share common information, independently of the database analyzed. The statistical similarity of the probability density distribution of one parameter for one database comparing with the others is also analyzed. Such statistical similarity analysis is performed through two-sample Kolmogorov-Smirnov test (KS) [47?9]. This method allows us to cluster some single features from a database. For graphical representation only, we have clustered the results when the feature is statistically similar between the databases. This non-parametric test evaluates the degree of similarity between two probability density functions. The null hypothesis H0 of the test means that two data distributions are from the same distribution. The alternative hypotheses H1 means that two data distributions are different. In our implementation, the significance level chosen is 5 . To accept the null hypothesis, the asymptotic p-value is calculated, which should be as near to 1 as possible. Such a p-value represents the probability that the null hypothesis is true by observing the extreme test under the null hypothesis. After estimating the feature distribution parameters, the mean, variance, skewness and kurtosis values of the distribution are provided for better knowledge of the feature distribution. The mean, variance and skewness indicate the symmetry of the distribution, and the kurtosis the peakedness of the distribution. The mean square difference between the parametric and non-parametric estimation is also given.ResultsThousands of features can be obtained from a signature to model its lexical morphology. In this section the lexical morphological features considered most relevant, i.e. descriptive and common, are described alongside their estimated PDFs. They are presented in a top-downPLOS ONE | DOI:10.1371/journal.pone.0123254 April 10,7 /Modeling the Lexical Morphology of Western Handwritten Signaturesprocess, starting from global feature characterization and finishing with specific details in the signature.Signature envelopeThe envelope of the signature is a fictitious shape which encloses each deposited signature. Each signature has its own specific envelope. In this study we have analyzed the average envelope of the signatures per databases by using the Active Shape Model (ASM). This me.
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