Search results for "PROBABILITY DENSITY"

Limit theorems and price changes in financial markets

1998

Abstract We discuss the relation between limit theorems in probability theory and price change statistics in financial markets. An analysis of the published empirical results and theoretical models show that the problem of the statistical properties of price (or index) changes is still open. By using the limit theorems of probability theory and the current assumption that stock prices are well described by martingales, we point out that the probability density function (PDF) of price changes is expected to belong to theclass of infinitely divisible PDFs.

Design and Simulation of Measurement-Based Correlation Models for Shadow Fading

2011

This paper deals with the design of measurement-based correlation models for shadow fading. Based on the correlation model, we design a simulation model using the sum-of-sinusoids (SOS) method to enable the simulation of spatial lognormal processes characterizing real-world shadow fading scenarios. The model parameters of the simulation model are computed by applying the Lp-norm method (LPNM). This method facilitates an excellent fitting of the simulation model’s autocorrelation function (ACF) to that of measured channels. Our study includes an evaluation of all important statistical quantities of the proposed measurement-based simulation model, such as the probability density function (PDF…

Tetrolet-based reduced reference image quality assessment approach

2014

In this paper, we propose a new reduced reference image quality assessment (RRIQA) scheme. For this purpose, we use a statistical-based method in a new adaptive Haar wavelet transform domain, called Tetrolet. Firstly, we decompose the reference and distorted images and we obtain the Tetrolet coefficients for each image. Secondly, we use a marginal Generalized Gaussian Density (GGD) to model each subband coefficients. Finally, the distortion measure is computed using the Kullback Leibler Divergence (KLD) between GGD Probability density function (PDFs). Experimental results show the efficiency of the proposed method when comparing to those reported in the literature.

A geometric street scattering channel model for car-to-car communication systems

2011

This paper presents a geometric street scattering channel model for car-to-car (C2C) communication systems under line-of-sight (LOS) and non-LOS (NLOS) propagation conditions. Starting from the geometric model, we develop a stochastic reference channel model, where the scatterers are uniformly distributed in rectangles in the form of stripes parallel to both sides of the street. We derive analytical expressions for the probability density functions (PDFs) of the angle-of-departure (AOD) and the angle-of-arrival (AOA). We also investigate the Doppler power spectral density (PSD) and the autocorrelation function (ACF) of the proposed model, assuming that the mobile transmitter (MT) and the mo…

Performance Analysis of M-DPSK Modulation over Fast-Hoyt Fading Channels under Non-Isotropic Scattering Conditions

2021

In this paper, we analyze the symbol error probability (SEP) performance of M-ary differential phase shift keying (M-DPSK) modulation schemes over frequency-flat fast-varying Hoyt multipath fading channels. Assuming general non-isotropic scattering conditions, we first derive a finite-range integral expression for the probability density function (PDF) of the phase difference between two non-isotropic Hoyt vectors perturbed by additive white Gaussian noise (AWGN). Based upon the theory of M-DPSK modulation and the obtained PDF formula, the SEP of M-DPSK and its corresponding asymptotic behavior in non-isotropic fast-Hoyt fading channels are derived. Specifically, a double semi-finite range …

Entropy, Benford’s first digit law, and the distribution of everything

2010

On the Statistical Properties of the Capacity of Spatially Correlated Nakagami-M MIMO Channels

2008

This paper studies the statistical properties of the channel capacity of spatially correlated Nakagami-m multiple- input multiple-output (MIMO) channels. We have derived closed- form expressions for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the lower bound on the channel capacity. In order to study the impact of the spatial correlation on the channel capacity, the analysis of the statistical properties of the channel capacity is carried out for different receiver antenna spacings. It is observed that the antenna spacing has a significant influence on the spread and maximum val…

On the statistical properties of the capacity of sparse multipath fading channels

2014

Most existing works in wireless communications assume rich scattering. However, there is growing experimental evidence that physical wireless channels can exhibit a sparse structure. By assuming an asymmetric Doppler power spectral density (PSD), we can model and simulate sparse channels by using a finite sum of weighted complex harmonic functions, also called sum of cisoids (SOC). In this paper, we focus on the analysis of the statistical properties of the instantaneous capacity of sparse SOC-based multipath fading channels under line-of-sight (LOS) conditions. The probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average…

Statistical Analysis of the Channel Capacity Outage Intervals in Massive MIMO Systems with OSTBC over Rayleigh Fading Channels

2015

This paper studies approximate solutions for the statistical properties of the outage intervals of the instantaneous capacity in massive multiple- input multiple- output (MIMO) sys- tems with orthogonal space-time block code (OSTBC) over Rayleigh fading channels. We take advantage from the fact that the probability density function (PDF) of the channel power gain can be approximated by a left-truncated Gaussian distribution if the number of transmit and receive antennas is large. Assuming a symmetrical Doppler power spectral density (PSD), a closed- form expression is presented for the Rice probability function of the outage durations. This function, in general, approximates the PDF of the …

On the statistical properties of the capacity of amplify-and-forward channels under LOS conditions

2008

Amplify-and-forward channels in cooperative networks provide a promising improvement in the network coverage and system throughput. Under line-of-sight (LOS) propagation conditions in such cooperative networks, the overall fading channel can be modeled by a double Rice process. In this article, we have studied the statistical properties of the capacity of double Rice fading channels. We have derived the analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. The obtained results are studied for different values of the amplitudes of the LOS components in …