1,724,004 research outputs found
Dagum vs. Singh-Maddala income distributions
No full textThis letter shows that the Dagum and the Singh-Maddala income distributions are closely related; it exploits this relationship to derive Lorenz ordering results for the Dagum distributions from known results for the Singh-Maddala family
Transmuted Singh-Maddala Distribution: A new Flexible and Upside-Down Bathtub Shaped Hazard Function Distribution
Full text linkThe Singh-Maddala distribution is very popular to analyze the data on income, expenditure, actuarial, environmental, and reliability related studies. To enhance its scope and application, we propose four parameters transmutedSingh-Maddala distribution, in this study. The proposed distribution is relatively more flexible than the parent distribution to model a variety of data sets. Its basic statistical properties, reliability function, and behaviors of the hazard function are derived. The hazard function showed the decreasing and an upside-down bathtub shape that is required in various survival analysis. The order statistics and generalized TL-moments with their special cases such as L-, TL-, LL-, and LH-moments are also explored. Furthermore, the maximum likelihood estimation is used to estimate the unknown parameters of the transmuted Singh-Maddala distribution. The real data sets are considered to illustrate the utility and potential of the proposed model. The results indicate that the transmuted Singh-Maddala distribution models the datasets better than its parent distribution.La distribución Singh-Maddala es muy popular para analizar datos deingresos, gastos, actuariales, ambientales y de confiabilidad.Para mejorar su alcance y aplicación se propone su extensión a la distribución de cuatro parámetros Singh-Maddala transmutada. Esta es más flexible en la modelación de diversos conjuntos de datos. Sus propiedades básicas, las funciones de confiabilidad y riesgos son estudiadas. La función de riesgo es decrecientes o tiene forma de bañera invertida. Como se requiere en varios estudios de sobrevivencia se exploran sus estadísticas de orden y los momentos TL, con sus casos especiales L, TL, LL y LH. Se emplea máxima verosimilitud para la estimación de los cuatro parámetros. Datos reales son usados para ilustrar la utilidad y potencialidad del modelo propuesto. Los resultados indican que la distribución propuesta ajusta mejor que la original
Extending Singh-Maddala Distribution
Full text linkA new distribution, the exponentiated transmuted Singh-Maddala distribution (ETSM), is presented, and three important special distributions are illustrated. Some mathematical properties are obtained, and parameters estimation method is applied using maximum likelihood. Illustrations based on random numbers and a real data set are given
SMFIT: Stata module to fit a Singh-Maddala distribution by maximum likelihood
No full textsmfit fits by ML the 3 parameter Singh-Maddala distribution to sample observations on a random variable. smpred calculates statistics summarizing a Singh-Maddala distribution which has been fitted using smfit. Unit record data are assumed (rather than grouped data).Singh-Maddala distribution, inequality, maximum likelihood
Simulation Studies Comparing Dagum and Singh-Maddala Income Distributions
Full text linkDagum and Singh–Maddala distributions have been widely assumed as models for income distribution in empirical analyses. The properties of these distributions are well known and several estimation methods for these distributions from grouped data have been discussed widely. Moreover, previous studies argue that the Dagum distribution gives a better fit than the Singh–Maddala distribution in the empirical analyses. This study explores the reason why Dagum distribution is preferred to the Singh–Maddala distribution in terms of the akaike information criterion through Monte Carlo experiments. In addition, the properties of the Gini coefficients and the top income shares from these distributions are examined by means of root mean square errors. From the experiments, we confirm that the fit of the distributions depends on the relationships and magnitudes of the parameters. Furthermore, we confirm that the root mean square errors of the Gini coefficients and top income shares depend on the relationships of the parameters when the data-generating processes are a generalized beta distribution of the second kind
SMGFIT: Stata module to fit a Singh-Maddala distribution to grouped data via ML
No full textsmgfit fits by ML the 3 parameter Singh-Maddala (1976) distribution to a sample of counts or frequencies by income category. (For an estimator designed for unit record data, ssc desc smfit). Optionally specified variables z1var and z2var encode the lower and upper limits of each interval; if they are not specified, variables serving that role and called z1 and z2 are assumed to exist.Singh-Maddala, income distribution, multinomial maximum likelihood, grouped, interval, censored
Heisenberg-Pauli-Weyl uncertainty inequalities and polynomial volume growth.
No full textIn this paper, we extend
the Heisenberg-Pauli-Weyl inequality to positive self-adjoint operators L on measure spaces with a "gauge function" such that (a) measures of balls are controlled by powers of the radius (possibly different powers for large and small balls); (b) the semigroup generated by L satisfies ultracontractive estimates with polynomial bounds of the same type. We give examples of applications of this result to sub-Laplacians on groups of polynomial volume growth and to certain higher-order left-invariant hypoelliptic operators on nilpotent groups. We finally show that these estimates also imply generalized forms of local uncertainty inequalities
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