The method of LQ-moments (LQMOM) for estimating parameters and quantiles of the Generalized Logistic (GL) distribution are introduced. We explore and extend class of LQMOM with consideration combinations of p and α values in the range 0 and 0.5. The popular quantile estimator namely the weighted kernel quantile (WKQ) estimator is proposed to estimate the quantile function. A comparison of these...

A spin chain, describing a nucleotides sequence, is identified by the the labels of a vector state of an irreducible representation of Uq→0(sl2). A master equation for the distribuion function is written, where the intensity of the one-spin flip is assumed to depend from the variation of the labels. The numerically computed equilibrium distribution is nicely fitted by a Yule distribution, which...

Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly maximum likelihood estimation (MLE). There will be discussed inexpensive density estimation, for example literally fitting a polynomial (or Fourier series) to the ...

We consider estimation of the covariance matrix of a random vector under the constraint that certain elements in the covariance matrix are zero. Assuming that the random vector follows a multivariate normal distribution, in which case the model is also known as covariance graph model, we present a new algorithm for maximum likelihood estimation of the covariance matrix with zero pattern. We giv...

A versatile, systematic, and efficient line-fitting algorithm is presented, accommodating (1) errors in both coordinates (‘errors in the variables’), (2) correlation between the noise in the two coordinates (i.e., equal noise density ellipses that are not aligned with the coordinate axes), (3) heteroscedastic noise (different noise covariance matrices for different data points), and (4) outlier...

We obtain recombination rate distribution functions for all human chromosomes using an optimal quantization method. This non-parametric method allows us to control over-/under-fitting. The piece-wise constant recombination rate distribution functions are convenient to store and retrieve. Our experimental results showed more abrupt distribution functions than two recently published results. In t...

The probability of schedule overruns for construction and engineering projects can be ascertained using a ‘best fit’ probability distribution from an empirical distribution. The statistical characteristics of schedule overruns occurring in 276 Australian construction and engineering projects were analysed. Skewness and kurtosis values revealed that schedule overruns are non-Gaussian. Theoretica...

This paper describes a novel moment matching based fitting method for phase-type (PH) distributions. A special sub-class of phase-type distributions is introduced for the fitting, called generalized hyper-Erlang distributions. The user has to provide only two parameters: the number of moments to match, and the upper bound for the sum of the multiplicities of the eigenvalues of the distribution,...

We introduce and evaluate via a Monte Carlo study a robust new estimation technique that fits distribution functions to grouped response time (RT) data, where the grouping is determined by sample quantiles. The new estimator, quantile maximum likelihood (QML), is more efficient and less biased than the best alternative estimation technique when fitting the commonly used ex-Gaussian distribution...

We inverse the surface gravity data to recover subsurface 3D density distribution with two strategy. In the first strategy, we assumed wide density model bound for inverting gravity data and In the second strategy, the inversion procedure have been carried out by limited bound density. Wediscretize the earth model into rectangular cells of constant andunidentified density. The number of cells i...