The exponentiated gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called Transmuted exponentiated gamma (TEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the TEG distribution is prov...

L (Linear) moments are used in identifying regional flood frequency distributions for different zones Tunisia wide. 1134 site-years of annual maximum stream flow data from a total of 42 stations with an average record length of 27 years are considered. The country is divided into two homogeneous regions (northern and central/southern Tunisia) using a heterogeneity measure, based on the spread o...

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...

This paper derives asymptotic normality of a class of M-estimators in the generalized autoregressive conditional heteroskedastic ~GARCH! model+ The class of estimators includes least absolute deviation and Huber’s estimator in addition to the well-known quasi maximum likelihood estimator+ For some estimators, the asymptotic normality results are obtained only under the existence of fractional u...

We show that the generating functions of the generalized Catalan numbers can be identified with the moment generating functions of probability density functions related to the Brownian motion stochastic process. Specifically, the probability density functions are exponential mixtures of inverse Gaussian (EMIG) probability density functions, which arise as the first passage time distributions to...

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble-averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different a...

Sharp lower and upper bounds for quasiconvex moments of generalized order statistics are proven by the use of the rearranged Moriguti’s inequality. Even in the second moment case, the method yields improvements of known quantile and moment bounds for the expectation of order and record statistics based on independent identically distributed random variables. The bounds are attainable providing ...

In this note we prove a generalization of the flat extension theorem of Curto and Fialkow (Memoirs of the American Mathematical Society, vol. 119. American Mathematical Society, Providence, 1996) for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free setting, ...

When σ is a quasi-definite moment functional with the monic orthogonal polynomial system {Pn(x)}∞n=0, we consider a point masses perturbation τ of σ given by τ := σ+ λ ∑m l=1 ∑ml k=0((−1) ulk/k!)δ (x− cl), where λ, ulk, and cl are constants with ci = cj for i = j. That is, τ is a generalized Uvarov transform of σ satisfying A(x)τ = A(x)σ, where A(x) = ∏m l=1(x− cl) l. We find necessary and suff...

This paper proposes model selection criteria ~MSC! for unconditional moment models using generalized empirical likelihood ~GEL! statistics+ The use of GELstatistics in lieu of J-statistics ~in the spirit of Andrews, 1999, Econometrica 67, 543–564; and Andrews and Lu, 2001, Journal of Econometrics 101, 123–164! leads to an alternative interpretation of the MSCs that emphasizes the common informa...