Stability of Random Sums and Extremes

This study is about the stability of random sums and extremes.The difficulty in finding exact sampling distributions resulted in considerable problems of computing probabilities concerning the sums that involve a large number of terms.Functions of sample observations that are natural interest other than the sum,are the extremes,that is , the minimum and the maximum of the observations.Extreme value distributions also arise in problems like the study of size effect on material strengths,the reliability of parallel and series systems made up of large number of components,record values and assessing the levels of air pollution.It may be noticed that the theories of sums and extremes are mutually connected.For instance,in the search for asymptotic normality of sums ,it is assumed that at least the variance of the population is finite.In such cases the contributions of the extremes to the sum of independent and identically distributed(i.i.d) r.vs is negligible.

Photoconductivity studies on some semiconducting thin films for photovoltaic applications

Photoconductivity (PC) processes may be the most suitable technique for obtaining information about the states in the gap. It finds applications in photovoItaics, photo detection and radiation measurements. The main task in the area of photovoltaics, is to increase the efficiency of the device and also to develop new materials with good optoelectronic properties useful for energy conversion, keeping the idea of cost effectiveness. Photoconduction includes generation and recombination of carriers and their transport to the electrodes. So thermal relaxation process, charge carrier statistics, effects of electrodes and several mechanisms of recombination are involved in photoconductivity.A major effect of trapping is to make the experimentally observed decay time of photocurrent, longer than carrier lifetime. If no trapping centers are present, then observed photocurrent will decay in the same way as the density of free carriers and the observed decay time will be equal to carrier lifetime. If the density of free carriers is much less than density of trapped carriers, the entire decay of photocurrent is effectively dominated by the rate of trap emptying rather than by the rate of recombination.In the present study, the decay time of carriers was measured using photoconductive decay (PCD) technique. For the measurements, the film was loaded in a liquid Helium cryostat and the temperature was controlled using Lakshore Auto tuning temperature controller (Model 321). White light was used to illuminate the required area of the sample. Heat radiation from the light source was avoided by passing the light beam through a water filter. The decay current. after switching off the illumination. was measured using a Kiethely 2000 multi meter. Sets of PCD measurements were taken varying sample temperature, sample preparation temperature, thickness of the film, partial pressure of Oxygen and concentration of a particular element in a compound. Decay times were calculated using the rate window technique, which is a decay sampling technique particularly suited to computerized analysis. For PCD curves with two well-defined regions, two windows were chosen, one at the fast decay region and the other at the slow decay region. The curves in a particular window were exponentially fitted using Microsoft Excel 2000 programme. These decay times were plotted against sample temperature and sample preparation temperature to study the effect of various defects in the film. These studies were done in order to optimize conditions of preparation technique so as to get good photosensitive samples. useful for photovoltaic applications.Materials selected for the study were CdS, In2Se3, CuIn2Se3 and CuInS2• Photoconductivity studies done on these samples are organised in six chapters including introduction and conclusion.

Statistics of avalanches in martensitic transformations, II. Modelling

Using a scaling assumption, we propose a phenomenological model aimed to describe the joint probability distribution of two magnitudes A and T characterizing the spatial and temporal scales of a set of avalanches. The model also describes the correlation function of a sequence of such avalanches. As an example we study the joint distribution of amplitudes and durations of the acoustic emission signals observed in martensitic transformations [Vives et al., preceding paper, Phys. Rev. B 52, 12 644 (1995)].

Agricultural practices and horizontal nutrient balances in urban gardens and the alternative use of urban agricultural land in Khartoum, Sudan

The surge in the urban population evident in most developing countries is a worldwide phenomenon, and often the result of drought, conflicts, poverty and the lack of education opportunities. In parallel with the growth of the cities is the growing need for food which leads to the burgeoning expansion of urban and peri-urban agriculture (UPA). In this context, urban agriculture (UA) contributes significantly to supplying local markets with both vegetable and animal produce. As an income generating activity, UA also contributes to the livelihoods of poor urban dwellers. In order to evaluate the nutrient status of urban soils in relation to garden management, this study assessed nutrient fluxes (inputs and outputs) in gardens on urban Gerif soils on the banks of the River Nile in Khartoum, the capital city of Sudan. To achieve this objective, a preliminary baseline survey was carried out to describe the structure of the existing garden systems. In cooperation with the author of another PhD thesis (Ms. Ishtiag Abdalla), alternative uses of cow dung in brick making kilns in urban Khartoum were assessed; and the socio-economic criteria of the brick kiln owners or agents, economical and plant nutritional value of animal dung and the gaseous emission related to brick making activities were assessed. A total of 40 household heads were interviewed using a semi-structured questionnaire to collect information on demographic, socio-economic and migratory characteristics of the household members, the gardening systems used and the problems encountered in urban gardening. Based on the results of this survey, gardens were divided into three groups: mixed vegetable-fodder gardens, mixed vegetable-subsistence livestock gardens and pure vegetable gardens. The results revealed that UA is the exclusive domain of men, 80% of them non-native to Khartoum. The harvested produce in all gardens was market oriented and represented the main source of income for 83% of the gardeners. Fast growing leafy vegetables such as Jew’s mallow (Corchorous olitorius L.), purslane (Portulaca oleracea L.) and rocket (Eruca sativa Mill.) were the dominant cultivated species. Most of the gardens (95%) were continuously cultivated throughout the year without any fallow period, unless they were flooded. Gardeners were not generally aware of the importance of crop diversity, which may help them overcome the strongly fluctuating market prices for their produce and thereby strengthen the contributions of UA to the overall productivity of the city. To measure nutrient fluxes, four gardens were selected and their nutrients inputs and outputs flows were monitored. In each garden, all plots were monitored for quantification of nutrient inputs and outputs. To determine soil chemical fertility parameters in each of the studied gardens, soil samples were taken from three selected plots at the beginning of the study in October 2007 (gardens L1, L2 and H1) and in April 2008 (garden H2) and at the end of the study period in March 2010. Additional soil sampling occurred in May 2009 to assess changes in the soil nutrient status after the River Nile flood of 2008 had receded. Samples of rain and irrigation water (river and well-water) were analyzed for nitrogen (N), phosphorus (P), potassium (K) and carbon (C) content to determine their nutrient inputs. Catchment traps were installed to quantify the sediment yield from the River Nile flood. To quantify the nutrient inputs of sediments, samples were analyzed for N, P, K and organic carbon (Corg) content, cation exchange capacity (CEC) and the particle size distribution. The total nutrient inputs were calculated by multiplying the sediment nutrient content by total sediment deposits on individual gardens. Nutrient output in the form of harvested yield was quantified at harvest of each crop. Plant samples from each field were dried, and analyzed for their N, P, K and Corg content. Cumulative leaching losses of mineral N and P were estimated in a single plot in garden L1 from December 1st 2008 to July 1st 2009 using 12 ion exchange resins cartridges. Nutrients were extracted and analyzed for nitrate (NO3--N), ammonium (NH4+-N) and phosphate PO4-3-P. Changes in soil nutrient balance were assessed as inputs minus outputs. The results showed that across gardens, soil N and P concentrations increased from 2007 to 2009, while particle size distribution remained unchanged. Sediment loads and their respective contents of N, P and Corg decreased significantly (P < 0.05) from the gardens of the downstream lowlands (L1 and L2) to the gardens of the upstream highlands (H1 and H2). No significant difference was found in K deposits. None of the gardens received organic fertilizers and the only mineral fertilizer applied was urea (46-0-0). This equaled 29, 30, 54, and 67% of total N inputs to gardens L1, L2, H1, and H2, respectively. Sediment deposits of the River Nile floods contributed on average 67, 94, 6 and 42% to the total N, P, K and C inputs in lowland gardens and 33, 86, 4 and 37% of total N, P, K and C inputs in highland gardens. Irrigation water and rainfall contributed substantially to K inputs representing 96, 92, 94 and 96% of total K influxes in garden L1, L2, H1 and H2, respectively. Following the same order, total annual DM yields in the gardens were 26, 18, 16 and 1.8 t ha-1. Annual leaching losses were estimated to be 0.02 kg NH4+-N ha-1 (SE = 0.004), 0.03 kg NO3--N ha-1 (SE = 0.002) and 0.005 kg PO4-3-P ha-1 (SE = 0.0007). Differences between nutrient inputs and outputs indicated negative nutrient balances for P and K and positive balances of N and C for all gardens. The negative balances in P and K call for adoptions of new agricultural techniques such as regular manure additions or mulching which may enhance the soil organic matter status. A quantification of fluxes not measured in our study such as N2-fixation, dry deposition and gaseous emissions of C and N would be necessary to comprehensively assess the sustainability of these intensive gardening systems. The second part of the survey dealt with the brick making kilns. A total of 50 brick kiln owners/or agents were interviewed from July to August 2009, using a semi-structured questionnaire. The data collected included general information such as age, family size, education, land ownership, number of kilns managed and/or owned, number of months that kilns were in operation, quantity of inputs (cow dung and fuel wood) used, prices of inputs and products across the production season. Information related to the share value of the land on which the kilns were built and annual income for urban farmers and annual returns from dung for the animal raisers was also collected. Using descriptive statistics, budget calculation and Gini coefficient, the results indicated that renting the land to brick making kilns yields a 5-fold higher return than the rent for agriculture. Gini coefficient showed that the kiln owners had a more equal income distribution compared to farmers. To estimate emission of greenhouse gases (GHGs) and losses of N, P, K, Corg and DM from cow dung when used in brick making, samples of cow dung (loose and compacted) were collected from different kilns and analyzed for their N, P, K and Corg content. The procedure modified by the Intergovernmental Panel on Climate Change (IPCC, 1994) was used to estimate the gaseous emissions of cow dung and fuel wood. The amount of deforested wood was estimated according to the default values for wood density given by Dixon et al. (1991) and the expansion ratio for branches and small trees given by Brown et al. (1989). The data showed the monetary value of added N and P from cow dung was lower than for mineral fertilizers. Annual consumption of compacted dung (381 t DM) as biomass fuel by far exceeded the consumption of fuel wood (36 t DM). Gaseous emissions from cow dung and fuel wood were dominated by CO2, CO and CH4. Considering that Gerif land in urban Khartoum supports a multifunctional land use system, efficient use of natural resources (forest, dung, land and water) will enhance the sustainability of the UA and brick making activities. Adoption of new kilns with higher energy efficiency will reduce the amount of biomass fuels (cow dung and wood) used the amount of GHGs emitted and the threat to the few remaining forests.

Surface Reflectance Recognition and Real-World Illumination Statistics

Humans distinguish materials such as metal, plastic, and paper effortlessly at a glance. Traditional computer vision systems cannot solve this problem at all. Recognizing surface reflectance properties from a single photograph is difficult because the observed image depends heavily on the amount of light incident from every direction. A mirrored sphere, for example, produces a different image in every environment. To make matters worse, two surfaces with different reflectance properties could produce identical images. The mirrored sphere simply reflects its surroundings, so in the right artificial setting, it could mimic the appearance of a matte ping-pong ball. Yet, humans possess an intuitive sense of what materials typically "look like" in the real world. This thesis develops computational algorithms with a similar ability to recognize reflectance properties from photographs under unknown, real-world illumination conditions. Real-world illumination is complex, with light typically incident on a surface from every direction. We find, however, that real-world illumination patterns are not arbitrary. They exhibit highly predictable spatial structure, which we describe largely in the wavelet domain. Although they differ in several respects from the typical photographs, illumination patterns share much of the regularity described in the natural image statistics literature. These properties of real-world illumination lead to predictable image statistics for a surface with given reflectance properties. We construct a system that classifies a surface according to its reflectance from a single photograph under unknown illuminination. Our algorithm learns relationships between surface reflectance and certain statistics computed from the observed image. Like the human visual system, we solve the otherwise underconstrained inverse problem of reflectance estimation by taking advantage of the statistical regularity of illumination. For surfaces with homogeneous reflectance properties and known geometry, our system rivals human performance.

Policy Improvement for POMDPs Using Normalized Importance Sampling

We present a new method for estimating the expected return of a POMDP from experience. The estimator does not assume any knowle ge of the POMDP and allows the experience to be gathered with an arbitrary set of policies. The return is estimated for any new policy of the POMDP. We motivate the estimator from function-approximation and importance sampling points-of-view and derive its theoretical properties. Although the estimator is biased, it has low variance and the bias is often irrelevant when the estimator is used for pair-wise comparisons.We conclude by extending the estimator to policies with memory and compare its performance in a greedy search algorithm to the REINFORCE algorithm showing an order of magnitude reduction in the number of trials required.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent years but at the moment few applications concern the description of natural phenomena with this type of probability models, as well as the interpretation of their parameters. The skew–normal distributions family represents an extension of the normal family to which a parameter (λ) has been added to regulate the skewness. The development of this theoretical field has followed the general tendency in Statistics towards more flexible methods to represent features of the data, as adequately as possible, and to reduce unrealistic assumptions as the normality that underlies most methods of univariate and multivariate analysis. In this paper an investigation on the shape of the frequency distribution of the logratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells, has been performed. Samples have been collected around the active center of Vulcano island (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals of about six months. Data of the logratio have been tentatively modeled by evaluating the performance of the skew–normal model for each well. Values of the λ parameter have been compared by considering temperature and spatial position of the sampling points. Preliminary results indicate that changes in λ values can be related to the nature of environmental processes affecting the data

SPSS Statistics Coach - An animated guide

What test for your data? SPSS Statistics Coach can help

Intro Statistics for MSc Students

Exercises and solutions for an introductory statistics course for MSc students. Diagrams for the questions are all together in the support.zip file, as .eps files