On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

Transient electric field distribution within the working volume of an NEMP simulator

Nuclear electro-magnetic pulse (NEMP) simulators which are used in the simulation of transient electromagnetic fields due to a high altitude nuclear detonation are generally excited with a double exponential high voltage pulse. This results in a current distribution on the wires of the simulator and hence a transient electric field in the working volume of the simulator where the test object is kept. It is found that for the simulator under study, the current distribution is non-uniform and so is the field distribution along the width of the simulator in the working volume. To make the current distribution uniform, several methods have been suggested and the results of these methods are analyzed and suitable conclusions are arrived at from those results.

Reconstructing The Vertical Distribution Of The Aeolian Saltation Mass Flux Based On The Probability Distribution Of Lift-Off Velocity

The probability distribution of lift-off velocity of the saltating grains is a bridge to linking microscopic and macroscopic research of aeolian sand transport. The lift-off parameters of saltating grains (i.e., the horizontal and vertical lift-off velocities, resultant lift-off velocity, and lift-off angle) in a wind tunnel are measured by using a Phase Doppler Particle Analyzer (PDPA). The experimental results show that the probability distribution of horizontal lift-off velocity of saltating particles on a bed surface is a normal function, and that of vertical lift-off velocity is an exponential function. The probability distribution of resultant lift-off velocity of saltating grains can be expressed as a log-normal function, and that of lift-off angle complies with an exponential function. A numerical model for the vertical distribution of aeolian mass flux based on the probability distribution of lift-off velocity is established. The simulation gives a sand mass flux distribution which is consistent with the field data of Namikas (Namikas, S.L., 2003. Field measurement and numerical modelling of acolian mass flux distributions on a sandy beach, Sedimentology 50, 303-326). Therefore, these findings are helpful to further understand the probability characteristics of lift-off grains in aeolian sand transport. (c) 2007 Elsevier B.V. All rights reserved.

Biology and distribution of grouper (Epinephelus coioides) in province waters (Abadan Bhrakan)

This survay has been done from Januray 2000 till May 2002 in Khouzestan costal waters. Four species of grouper were identified from which orange spotted grouper (Epinephelus coioides) was the dominant species. For studing environmental parameters and reproductive biology, age, growth parameters and mortality rate samples were collected by fishing ship. Samples were taken montly in 4 days by fishing traps and trawls. In addition, some samples were obtained from Khozestan fish landing centres. Environmental factors such as PH, 02, salinity, water temperature and depth of traping areas, were measured. To identify species, morphometric characteries of 452 individal fishes were measured. Stomach contents of 394 fish were has survaid, from which stomach of 226 fish, and 168 fish had empty stomachs. Percentage of empty stomachs (cv) in males was more than females. Food items found in 73 percent of stomach were crab (11%), shrimps (8.8%) , squids (3.9%), gastropods (17%) and bivalves (0.4%). Feeding intensity in year classes did not obay logic trends The importance relatively indicator (I.R.I) were 81, 9.9, 4, 1.5 and 0.3 percent for fish, crab, shrimp, squid, gastropod and bivalve respectively. For age determination, sagita otoliths of 450 fish were taken and countable sections were obtained from 425 specimens. Relative frequency distribution of opaque and transparent rings showed that each opaque growth ring generates once a year from November to September. It seemed that generation of opaque rings is affected by temperature and photoperiod changes. Correlation between length and age was calculated using Von Bertalanffy's least square method. Following equasion was obtaind: L(t) : 122.27 (1 e 0.146 (t+0.482)) Growth parameters were determined through by Ford Walford equasion and Response Surface and Shepherd subcommands in Elefan program and L00 and K amounts were have determined. Correlation between length and age of 635 fish was determined by gender . Length and age correlation was calculated by exponential model and between total length and standard length by straghit line model. Correlation between age and weight of sagita was calculated by total length and age. The most Correlation was between sagita weight and fish age (r=0.876). Total mortality rate (z) was estimated by Length Converthed Method , Jones and Vanzaling and Powel Wetherall. Total mortality rate was z=0.39. Natural mortality rate, using Pauly method was calculated M=0.32. Fishing mortality (F) was 0.08. Gonads of 425 fishes were surveid within 18 month, from which 363 were female, 46 were male and 16 were sex reversing individuals .Total length of females varied from 26 to 95.5 centimeters while males length varied from 56.5 to 107 centimeters. Sex reversing individuals had a length of 47.5 centimeters, when two years old and 62.5 centimeters at age of 3 years. From the mentioned 425 fish, 401 individuals were matured, containing 339 females and 62 males, 5.47 females against each male. Montly changes of Gonadosomatic Index (GSI) by total body weight and standard length and total body length showed that this index increases from march to May and maximum increase was in May . This experiment was adapted in spawning season. Potential, relative, and absoulate fecundity was estimated by counting eggs in three samples. Total amount of traped fish using special traps was 16182.18 kg from which Epinephelus coioides provided catching 15353.43 kg of it (91.27 %) and By catch was 141.18 kg (8.24 %). Total average CPUE for whole catch was 123.33 kg/day/vessel. Total amount of catch was estimated 232.04 tons, considering CPUE of total catch and total Khuzestan trap ships effort.

incomplete exponential sums over galois rings with applications to some binary sequences derived from z(2l)

IEEE Computer Society

Distribution characteristics of (CS)-C-137 in wind-eroded soil profile and its use in estimating wind erosion modulus

Due to its inert reaction in soil system and distinctive vertical distribution in soil profile, caesium-137 (Cs-137) has been used as a tracer to assess wind erosion. In this study, 62 soil samples were collected from 4 sampling sites in Taipusi County, Inner Mongolia; Caesium-137 activities for those soil samples were measured using a gamma-ray spectrometry in Sichuan University, Chengdu. Distribution pattern of Cs-137 in vertical soil profile was different for different land use and land cover types. Caesium-137 was distributed homogeneously in plow layer of cropland, and negatively exponential in low to medium cover grassland. Distribution pattern in high covered grassland was represented by a peak at 2-4 cm soil depth followed by a negative exponential curve. Based on those findings, simplified mass balance model was chosen to estimate the rate of wind erosion for cropland, while profile distribution model was used for grassland. Estimated wind erosion rates were 7990, 4270 and 1808 Mg(.)km(-2.)a(-1) for cropland, low cover grassland and medium cover grassland, respectively. Wind erosion intensity correlated negatively with plant cover.

Exploring the Origin of Power Law Distribution in Single-Molecule Conformation Dynamics: Energy Landscape Perspectives

We explored the origin of power law distribution observed in single-molecule conformational dynamics experiments. By establishing a kinetic master equation approach to study statistically the microscopic state dynamics, we show that the underlying landscape with exponentially distributed density of states leads to power law distribution of kinetics. The exponential density of states emerges when the system becomes glassy and landscape becomes rough with significant trapping.

Plankton Of The Fladen Ground During Flex-76 .3. Vertical-Distribution Population-Dynamics And Production Of Calanus-Finmarchicus (Crustacea Copepoda)

Samples taken in the northern North Sea with the Continuous Plankton Recorder (CPR), the Undulating Oceanographic Recorder (UOR), the Longhurst Hardy Plankton Recorder (LHPR) and by our colleagues from other participating Institutes during the Fladen Ground Experiment (FLEX 76) were used to describe the vertical distribution and population dynamics of Calanus finmarchicus (Gunnerus) and to provide estimates of the production and carbon budget of the population from 19 March to 3 June, 1976. Total production of the 19 March to 3 June, 1976. Total production of the nauplii and copepodite stages (including adults), during the exponential growth phase in May, was estimated to be in the range of 0.49 to 0.91 g C m-2 d-1 or 29.0 to 55 g dry wt m-2 (14.5 to 27.8 g C m-2) for the three successive 10 d periods in May. Two gross growth efficiencies (K 1) (20 and 34%), together with the lower value of C. finmarchicus production, were used to calculate the gross ingestion levels of algae as 2.45 and 1.44 g C m-2 d-1 (73.5 and 43.2 g C m-2 over the May period). These ingestion levels, together with the algae ingested by other zooplankton species, are greater than the estimated total phytoplankton production of 45.9 g C m-2 over the FLEX period. A number of factors are discussed which could explain the discrepancies between the production estimates. One suggestion is that the vertical distribution of the development stages of this herbivorous copepod and their diel and ontogenetic migration patterns enable it to efficiently exploit its food source. Data from the FLEX experiment indicated that the depletion of nutrients limited the size of the spring bloom, but that it was the grazing pressure exerted by C. finmarchicus which was responsible for the control and depletion of the phytoplankton in the spring of 1976 in the northern North Sea.

Abrasion, transport and distribution of sediment in selected streams of Southern Ontario and Western New York /

The rate of decrease in mean sediment size and weight per square metre along a 54 km reach of the Credit River was found to depend on variations in the channel geometry. The distribution of a specific sediment size consist of: (1) a transport zone; (2) an accumulation zone; and (3) a depletion zone. These zones shift downstream in response to downcurrent decreases in stream competence. Along a .285 km man-made pond, within the Credit River study area, the sediment is also characterized by downstream shifting accumulation zones for each finer clast size. The discharge required to initiate movement of 8 cm and 6 cm blocks in Cazenovia Creek is closely approximated by Baker and Ritter's equation. Incipient motion of blocks in Twenty Mile Creek is best predicted by Yalin's relation which is more efficient in deeper flows. The transport distance of blocks in both streams depends on channel roughness and geometry. Natural abrasion and distribution of clasts may depend on the size of the surrounding sediment and variations in flow competence. The cumulative percent weight loss with distance of laboratory abraded dolostone is defined by a power function. The decrease in weight of dolostone follows a negative exponential. In the abrasion mill, chipping causes the high initial weight loss of dolostone; crushing and grinding produce most of the subsequent weight loss. Clast size was found to have little effect on the abrasion of dolostone within the diameter range considered. Increasing the speed of the mill increased the initial amount of weight loss but decreased the rate of abrasion. The abrasion mill was found to produce more weight loss than stream action. The maximum percent weight loss determined from laboratory and field abrasion data is approximately 40 percent of the weight loss observed along the Credit River. Selective sorting of sediment explains the remaining percentage, not accounted for by abrasion.

Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).

Bayesian Inference in Exponential and Pareto populations in the presence of Outliers

This thesis Entitled Bayesian inference in Exponential and pareto populations in the presence of outliers. The main theme of the present thesis is focussed on various estimation problems using the Bayesian appraoch, falling under the general category of accommodation procedures for analysing Pareto data containing outlier. In Chapter II. the problem of estimation of parameters in the classical Pareto distribution specified by the density function. In Chapter IV. we discuss the estimation of (1.19) when the sample contain a known number of outliers under three different data generating mechanisms, viz. the exchangeable model. Chapter V the prediction of a future observation based on a random sample that contains one contaminant. Chapter VI is devoted to the study of estimation problems concerning the exponential parameters under a k-outlier model.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

Bimodal extension based on the skew-normal distribution with application to pollen data

This paper considers an extension to the skew-normal model through the inclusion of an additional parameter which can lead to both uni- and bi-modal distributions. The paper presents various basic properties of this family of distributions and provides a stochastic representation which is useful for obtaining theoretical properties and to simulate from the distribution. Moreover, the singularity of the Fisher information matrix is investigated and maximum likelihood estimation for a random sample with no covariates is considered. The main motivation is thus to avoid using mixtures in fitting bimodal data as these are well known to be complicated to deal with, particularly because of identifiability problems. Data-based illustrations show that such model can be useful. Copyright (C) 2009 John Wiley & Sons, Ltd.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.