Estimating Lorenz Curves Using a Dirichlet Distribution

The Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares assuming that the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology which recognizes the cumulative proportional nature of the Lorenz curve data by assuming that the proportion of income is distributed as a Dirichlet distribution. Five Lorenz-curve specifications were used to demonstrate the technique. Once a likelihood function and the posterior probability density function for each specification are derived we can use maximum likelihood or Bayesian estimation to estimate the parameters. Maximum likelihood estimates and Bayesian posterior probability density functions for the Gini coefficient are also obtained for each Lorenz-curve specification.

The Transit Light Curve Project. IX. Evidence for a Smaller Radius of the Exoplanet XO-3b

We present photometry of 13 transits of XO-3b, a massive transiting planet on an eccentric orbit. Previous data led to two inconsistent estimates of the planetary radius. Our data strongly favor the smaller radius, with increased precision: R_p = 1.217 +/- 0.073 R_Jup. A conflict remains between the mean stellar density determined from the light curve, and the stellar surface gravity determined from the shapes of spectral lines. We argue the light curve should take precedence, and revise the system parameters accordingly. The planetary radius is about 1 sigma larger than the theoretical radius for a hydrogen-helium planet of the given mass and insolation. To help in planning future observations, we provide refined transit and occultation ephemerides.Comment: To appear in ApJ [22 pages

Using conditional kernel density estimation for wind power density forecasting

Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this paper, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our interest is in intraday data and prediction from 1 to 72 hours ahead. We model wind power in terms of wind speed and wind direction. In this framework, there are two key uncertainties. First, there is the inherent uncertainty in wind speed and direction, and we model this using a bivariate VARMA-GARCH (vector autoregressive moving average-generalized autoregressive conditional heteroscedastic) model, with a Student t distribution, in the Cartesian space of wind speed and direction. Second, there is the stochastic nature of the relationship of wind power to wind speed (described by the power curve), and to wind direction. We model this using conditional kernel density (CKD) estimation, which enables a nonparametric modeling of the conditional density of wind power. Using Monte Carlo simulation of the VARMA-GARCH model and CKD estimation, density forecasts of wind speed and direction are converted to wind power density forecasts. Our work is novel in several respects: previous wind power studies have not modeled a stochastic power curve; to accommodate time evolution in the power curve, we incorporate a time decay factor within the CKD method; and the CKD method is conditional on a density, rather than a single value. The new approach is evaluated using datasets from four Greek wind farms

A new approach to evaluate gamma-ray measurements

Misunderstandings about the term random samples its implications may easily arise. Conditions under which the phases, obtained from arrival times, do not form a random sample and the dangers involved are discussed. Watson's U sup 2 test for uniformity is recommended for light curves with duty cycles larger than 10%. Under certain conditions, non-parametric density estimation may be used to determine estimates of the true light curve and its parameters

A comparative study of monotone nonparametric kernel estimates

In this paper we present a detailed numerical comparison of three monotone nonparametric kernel regression estimates, which isotonize a nonparametric curve estimator. The first estimate is the classical smoothed isotone estimate of Brunk (1958). The second method has recently been proposed by Hall and Huang (2001) and modifies the weights of a commonly used kernel estimate such that the resulting estimate is monotone. The third estimate was recently proposed by Dette, Neumeyer and Pilz (2003) and combines density and regression estimation techniques to obtain a monotone curve estimate of the inverse of the isotone regression function. The three concepts are briefly reviewed and their finite sample properties are studied by means of a simulation study. Although all estimates are first order asymptotically equivalent (provided that the unknown regression function is isotone) some differences for moderate samples are observed. --isotonic regression,order restricted inference,Nadaraya-Watson estimator,local linear regression,monte carlo simulation

Dark baryons and rotation curves

The best measured rotation curve for any galaxy is that of the dwarf spiralXXXX DDO 154, which extends out to about 20 disk scale lengths. It provides an ideal laboratory for testing the universal density profile prediction from high resolution numerical simulations of hierarchical clustering in cold dark matter dominated cosmological models. We find that the observed rotation curve cannot be fit either at small radii, as previously noted, or at large radii. We advocate a resolution of this dilemma by postulating the existence of a dark spheroid of baryons amounting to several times the mass of the observed disk component and comparable to that of the cold dark matter halo component. Such an additional mass component provides an excellent fit to the rotation curve provided that the outer halo is still cold dark matter-dominated with a density profile and mass-radius scaling relation as predicted by standard CDM-dominated models. The universal existence of such dark baryonic spheroidal components provides a natural explanation of the universal rotation curves observed in spiral galaxies, may have a similar origin and composition to the local counterpart that has been detected as MACHOs in our own galactic halo via gravitational microlensing, and is consistent with, and even motivated by, primordial nucleosynthesis estimates of the baryon fraction.Comment: 16 pages LaTeX, 2 postscript figures. To be published in The Astrophysical Journal, Letter

Accurate simulation estimates of cloud points of polydisperse fluids

We describe two distinct approaches to obtaining cloud point densities and coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation within the grand canonical ensemble. The first method determines the chemical potential distribution $\mu(\sigma)$ (with $\sigma$ the polydisperse attribute) under the constraint that the ensemble average of the particle density distribution $\rho(\sigma)$ matches a prescribed parent form. Within the region of phase coexistence (delineated by the cloud curve) this leads to a distribution of the fluctuating overall particle density n, p(n), that necessarily has unequal peak weights in order to satisfy a generalized lever rule. A theoretical analysis shows that as a consequence, finite-size corrections to estimates of coexistence properties are power laws in the system size. The second method assigns $\mu(\sigma)$ such that an equal peak weight criterion is satisfied for p(n)$for all points within the coexistence region. However, since equal volumes of the coexisting phases cannot satisfy the lever rule for the prescribed parent, their relative contributions must be weighted appropriately when determining$\mu(\sigma)$. We show how to ascertain the requisite weight factor operationally. A theoretical analysis of the second method suggests that it leads to finite-size corrections to estimates of coexistence properties which are {\em exponentially small} in the system size. The scaling predictions for both methods are tested via Monte Carlo simulations of a novel polydisperse lattice gas model near its cloud curve, the results showing excellent quantitative agreement with the theory.Comment: 8 pages, 6 figure