Search results for "Variables"
showing 10 items of 578 documents
Fast equivariant JADE
2013
Independent component analysis (ICA) is a widely used signal processing tool having applications in various fields of science. In this paper we focus on affine equivariant ICA methods. Two such well-established estimation methods, FOBI and JADE, diagonalize certain fourth order cumulant matrices to extract the independent components. FOBI uses one cumulant matrix only, and is therefore computationally very fast. However, it is not able to separate identically distributed components which is a major drawback. JADE overcomes this restriction. Unfortunately, JADE uses a huge number of cumulant matrices and is computationally very heavy in high-dimensional cases. In this paper, we hybridize the…
On the Statistical Properties of Phase Crossings and Random FM Noise in Double Rayleigh Fading Channels
2016
In this paper, we study the statistics of phase processes and random frequency modulation (FM) noise encountered in double Rayleigh fading channels. The Rayleigh processes making up the double Rayleigh channel are assumed to be independent but not necessarily identically distributed. The Doppler power spectral densities of these processes are supposed to be symmetric about the carrier frequency. Under these fading conditions, we derive first an expression for the joint probability density function (jpdf) of the phase process and its rate of change. Capitalizing on this jpdf formula, we then investigate the probability density function (pdf) and cumulative distribution function (cdf) of rand…
Tests for time reversibility: a complementarity analysis
2003
Abstract Since time reversibility (TR) is a necessary condition for an independent and identically distributed (iid) sequence, several tests for TR have been suggested to be applied as tests for model misspecification. In this paper, we analyze possible complementarities among two well known TR tests (Ramsey and Rothman's test, and Chen et al.'s test) in two situations: (1) the fitted model is a linear ARMA model when the true data generating process is a nonlinear-in-mean model (either threshold autoregressive or bilinear), and (2) the fitted model is a symmetric GARCH model but the true process belongs to the asymmetric GARCH family (either EGARCH or GJR). The results suggest that there a…
Statistical Properties of Double Hoyt Fading With Applications to the Performance Analysis of Wireless Communication Systems
2018
In this paper, we investigate the statistical properties of double Hoyt fading channels, where the overall received signal is determined by the product of two statistically independent but not necessarily identically distributed single Hoyt processes. Finite-range integral expressions are first derived for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades of the envelope fading process. A closed-form approximate solution is also deduced for the LCR by making use of the Laplace approximation theorem. Applying the derived PDF of the double Hoyt channel, we then provide analytical expressions for the average…
Modelling the occurrence of rainy days under a typical Mediterranean climate
2014
The statistical inference of the alternation of wet and dry periods in daily rainfall records can be achieved through the modelling of inter-arrival time-series, IT, defined as the succession of times elapsed from a rainy day and the one immediately preceding it. In this paper, under the hypothesis that ITs are independent and identically distributed random variables, a modelling framework based on a generalisation of the commonly adopted Bernoulli process is introduced. Within this framework, the capability of three discrete distributions, belonging to the Hurwitz–Lerch-Zeta family, to reproduce the main statistical features of IT time-series was tested. These distributions namely Lerch-se…
Horizontal visibility graphs: exact results for random time series
2009
The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows us to apply methods of complex network theory for characterizing time series. In this work we present the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of our former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables). After presenting some properties of the algorithm, we present exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length. We sh…
Moments and Laws of Large Numbers
2020
The most important characteristic quantities of random variables are the median, expectation and variance. For large n, the expectation describes the typical approximate value of the arithmetic mean (X 1+…+X n )/n of independent and identically distributed random variables (law of large numbers).
Almost sure rates of mixing for i.i.d. unimodal maps
2002
International audience; It has been known since the pioneering work of Jakobson and subsequent work by Benedicks and Carleson and others that a positive measure set of quadratic maps admit an absolutely continuous invariant measure. Young and Keller-Nowicki proved exponential decay of its correlation functions. Benedicks and Young, and Baladi and Viana studied stability of the density and exponential rate of decay of the Markov chain associated to i.i.d. small perturbations. The almost sure statistical properties of the sample stationary measures of i.i.d. itineraries are more difficult to estimate than the "averaged statistics". Adapting to random systems, on the one hand partitions associ…
On the Statistical Analysis of Equal Gain Combining over Multiple Double Rice Fading Channels in Cooperative Networks
2010
This article analyzes the statistical properties of narrowband mobile-to-mobile (M2M) fading channels with equal gain combining (EGC) under line-of-sight (LOS) propagation conditions. Here, we study a dual-hop amplify-and-forward (AF)relay network. It is assumed that there can exist LOS components in the transmission links between the source mobile station and the destination mobile station via K mobile relays. In order to cater for asymmetric fading conditions in the relay links, the received signal envelope at the output of the equal gain (EG) combiner is thus modeled as a sum of K double Rice processes. These processes are considered to be independent but not necessarily identically dist…
Multilevel Methodology Approach for the Construction of Real Estate Monthly Index Numbers
2015
AbstractIn this paper, we evaluate price indices and hedonic price indices for Italian real estate data using multilevel models. The methodology is based on a random coefficient panel data model. We propose a Laspeyres-type price index and hedonic prices indexes based on some characteristics of the sold properties. The multilevel hierarchical analysis has the advantage of allowing the appraisal analysis for groups, and identified in the same sample data the hierarchical structures of market segmentation according to the parameters of the real estate segment. It allows getting a lot of regression functions as the number of groups identified. Obviously, this depends on the sample size and the…