A flexible distribution class for count data

The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-parameter generalization of the Poisson distribution that can accommodate data over- or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this model’s flexibility, encompassing several classical distributions as well as other count data distributions containing significant data dispersion

Analysis of Languages with Extreme Values in the Indices of Relativity, Density and Informative Efficiency: The Morphological and Genetic Typology and the Complexity of the Phonetic-Phonological System in the Study of the Number and Length of Words and Phonemes

El presente artículo analiza las correlaciones matemáticas entre las lenguas que presentan valores extremos en los llamados ‘índice de relatividad informativa’, ‘índice de densidad informativa’, ‘índice de eficiencia informativa léxica’ e ‘índice de eficiencia informativa fónica’. Dichos índices expresan los coeficientes resultantes de dividir el número de ‘tokens’ y el número de ‘unidades fónicas convencionales de token’, empleados para expresar una misma información. En el presente trabajo nos centramos muy especialmente en aquellas lenguas que muestran valores extremos en dichos indíces y analizamos en qué modo afectan la tipología morfológica o las características fonético-fonológicas de las lenguas a cuestiones como número total de palabras y fonemas, longitud de palabras o economía del lenguaje.This article analyses the mathematical correlations between languages which present extreme values in the so-called ‘index of informative relativity’, ‘index of informative density’, ‘lexical informative efficiency index’, and ‘phonic informative efficiency index’. These indices express the coefficients resulting from dividing the number of ‘tokens’ and number of ‘token conventional phonic units’, used to express the same information. In the present work we focus very especially on those languages that show extreme values in aforesaid indices and we analyze how the morphological typology or the phonetic-phonological characteristics of the languages affect issues such as the total number of words and phonemes, length of words or economy of language

The Effect of Neighborhood Size and Morphology in the Chinese Language

The Neighborhood Size Effect (NSE), characterized as the effect in word determination based on changing one orthographic aspect of that word. The amount of words that can be created through such manipulation is called a neighborhood size (NS). Number of other factors such as frequency, how often a word appears and morphology, the combination of meaningful word units, have been suggested to have an overriding effect on NSE. In addition, there is a lack of research on NSE with non-alphabetical languages such as Chinese, which uses characters comprising of a multitude of semantic or phonetic markers. In this experiment, participants coming from mainland China were presented with 60 individual characters and 59 characters with Chinese morphology made up of two characters which form single words. Both conditions, were manipulated with NS by adjusting the semantic or phonetical radical within a character and with frequency by using a website that measures how frequent a character appeared within the language. Both character conditions were found to have a significant effect with frequency and neighborhood size (NS) with characters with higher frequency and lower NS found to have higher accuracy and lower reaction times. With low frequency single characters, it was that those with higher neighborhood size had greater delay in reaction time and lower accuracy. With low frequency morphologically constructed characters, it was found that lower neighborhood size had higher accuracy, but no significant result with regards to reaction time. Due to differing accuracy results with NS and character condition, it is suggested that further factors such as morphological processing in single characters and bigram frequency in morphologically constructed characters might have an effect on word determination in conjunction with neighborhood size. Thus, it is a possibility that Chinese morphological may depend more on other factors than neighborhood size