The Weibull distribution, an extreme value distribution, is frequently used to model survival, reliability, wind speed, and other data. One reason for this is its flexibility; it can mimic various distributions like the exponential or normal. The two-parameter Weibull has a shape (γ) and scale (β) parameter. Parameter estimation has been an ongoing search to find efficient, unbiased, and minimal variance estimators. Through data analysis and simulation studies, the following three methods of estimation will be discussed and compared: maximum likelihood estimation (MLE), method of moments estimation (MME), and median rank regression (MRR). The analysis of wind speed data from the TW Daniels Experimental Forest are used for this study to test the performance and flexibility of the Weibull distribution.

En 1975 H. Fujimoto a généralisé les résultats d’unicité pour des fonctions holomorphes dus à Nevanlinna pour des applications méromorphes de Cn dans CPN. Il a démontré que pour deux applications méromorphes non linéairement dégénérées f et g de Cn dans CPN, si elles ont les mêmes images réciproques, comptées avec leurs multiplicités, par rapport à (3N + 2) hyperplans de CPN en position générale, alors f g. Depuis, ce problème a été étudié d’une manière intensive par H. Fujimoto, W. Stoll, L. Smiley, M. Ru, G. Dethloff-T.V.Tan, D.D.Thai-S.D.Quang, Chen-Yan et d’autres auteurs. En parallèle avec le développement de la théorie de Nevanlinna, la théorie de distribution des valeurs de l’application de Gauss des surfaces minimales dans Rm a été étudiée d’une manière intensive par R.Osserman, S.S. Chern, F. Xavier, H. Fujimoto, S.J. Kao, M. Ru et d’autres auteurs. Dans cette thèse, nous avons continué d’étudier ces problèmes. Nous avons obtenu les résultats principaux suivants: +) Théorèmes d’unicité avec multiplicités tronquées des applications méromorphes de Cn dans CPN ayant les mêmes images réciproques par rapport è (2N + 2) hyperplans de CPN. +) Théorèmes d’unicité avec multiplicités tronquées des applications méromorphes de Cn dans CPN ayant des cibles mobiles et un ensemble d’identité petit. +) Théorèmes d’unicité avec multiplicités tronquées des applications méromorphes de Cn dans CPN ayant des cibles fixes ou mobiles et satisfaisant des conditions sur les dérivées. +) Théorèmes de ramification de l’application de Gauss de certaines classes de surfaces minimales complètes dans Rm (m = 3,4). / In 1975, H. Fujimoto generalized Nevanlinna’s known results for meromorphic fonctions to the case of meromorphic mappings of Cn into PN(C). He proved that for two linearly nondegenerate meromorphic mappings f and g of C into PN(C). if they have the saine inverse images counted with multiplicities for 3N + 2 hyperplanes in general position in PN(C) then f = g. After that, this problem has been studied intensively by a number of mathematicans as H. Fujimoto, W. Stoll, L. Smiley, M. Ru, G. Dethloff - T. V. Tan, D. D. Thai - S. D. Quang, Chen-Yan and so on. Parallel to the development of Nevanlinna theory, the value distribution theory of the Gauss map of minimal surfaces immersed in Rm vas studied by many mathematicans as R. Osserman, S.S. Chern, F. Xavier, H. Fujimoto, S. J. Kao, M. Ru and many other mathematicans. In this thesis, we continuous studing some problems on these directions. The main goals of the thesis are followings. • Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) sharing 2N + 2 fixed hyperplanes.• Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) for moving targets, and a small set of identity.

Master of Agribusiness / Department of Agricultural Economics / Vincent Amanor-Boadu / The purpose of this thesis was to estimate the value accruing to Zambian bean supply chain participants with the view to showing that value at the different stages is a function of the value addition and risk incurred at those stages. The data used in the study came from two different surveys done under the Pulse Value Chain Initiative – Zambia focusing on producers and bean traders. The surveys used structured questionnaires for both producers and traders. The producers were sampled from three principal bean producing provinces in Zambia: Lundazi, Mbala and Kalomo. The traders were sampled from the largest consumer region in the country – Lusaka – and focused on traders operating in the three principal markets in the city: Soweto; Chilenje; and Mtendere. The analyses were conducted using STATA®, employing both statistical and econometric methods. Value was defined as a function of transaction costs and value addition as well as the risks borne. In the Zambian mixed bean trade environment, where traders travel to remote locations where producers live and produce, they are seen to incur higher levels of risk and undertake higher levels of value addition – assembling the grain, bagging them and moving them from the rural areas where production occurs to the cities where customers reside. As such, it is expected that value creation and distribution would increase away from the farm. The results confirmed this expectation. The total average value created at the farm level was ZMK3,391.06/kg. However, the average value accruing to traders who only undertook wholesaling was ZMK7,405.75/kg while that accruing to traders going further down the chain to retail was ZMK9,663.56/kg. Traders who engaged in institutional trade produced an average value of ZMK8,750.75/kg. The share of total value produced accruing to producers in the producer-wholesaler-retailer chain was about 16.6 percent because of the higher value addition and risk that occur further downstream in the chain. The share of total value produced accruing to producers in the producer-wholesaler-institutional buyer chain was about 17.3 percent. The study showed that female producers’ share was not different, statistically speaking, from male producers’ value. It also showed that the average value created in thin (smaller) markets was higher than the value created in larger markets, probably because of the level of competition that occurs in the latter markets. Interestingly, the results showed that the larger the land holdings of producers, the lower the value created. This is in line with the foregoing results of size, competition and value. The study suggests that producers’ share of total value created may be enhanced by helping producers undertake specific activities that increased the value they added and reduce the risks that traders bear in their search for grain. One of such activities could be the formation of horizontal strategic alliances among producers that allowed producers to aggregate grain at particular locations in significant lots and bag them. This service would allow them to extract higher value from the exchange with traders. Any attempt to address the perceived “unfair” distribution of value along the supply chain by administrative fiat could result in higher costs to the whole supply chain and crate adverse unintended consequences for producers and the treasury.

In this article, we make inferences for the Weibull parameters and propose two test statistics for the comparison of two Weibull distributions based on interval-censored data. However, the distributions of the two statistics are unknown and not easy to obtain, therefore a simulation study is necessary. An urn model in the simulation of interval-censored data was proposed by Lee (1999) to select random intervals. Then we propose a simulation procedure with urn model to obtain approximately the quantiles of the two statistics. We demonstrate an example in AIDS study to illustrate how the tests can be applied to the infection time distributions of AIDS.

The presence of nonlinear dependence and chaos has strong implications for predictive modeling and the analysis of dominant processes in hydrology and climate. Analysis of extremes may aid in developing predictive models in hydro-climatology by giving enhanced understanding of processes driving the extremes and perhaps delineate possible anthropogenic or natural causes. This dissertation develops and utilizes different set of tools for predictive modeling, specifically nonlinear dependence, extreme, and chaos, and tests the viability of these tools on the real data. Commonly used dependence measures, such as linear correlation, cross-correlogram or Kendall's tau, cannot capture the complete dependence structure in data unless the structure is restricted to linear, periodic or monotonic. Mutual information (MI) has been frequently utilized for capturing the complete dependence structure including nonlinear dependence. Since the geophysical data are generally finite and noisy, this dissertation attempts to address a key gap in the literature, specifically, the evaluation of recently proposed MI-estimation methods to choose the best method for capturing nonlinear dependence, particularly in terms of their robustness for short and noisy data. The performance of kernel density estimators (KDE) and k-nearest neighbors (KNN) are the best for 100 data points at high and low noise-to-signal levels, respectively, whereas KNN is the best for 1000 data points consistently across noise levels. One real application of nonlinear dependence based on MI is to capture extrabasinal connections between El Nino-Southern Oscillation (ENSO) and river flows in the tropics and subtropics, specifically the Nile, Amazon, Congo, Parana, and Ganges rivers which reveals 20-70% higher dependence than those suggested so far by linear correlations. For extremes analysis, this dissertation develops a new measure precipitation extremes volatility index (PEVI), which measures the variability of extremes, is defined as the ratio of return levels. Spatio-temporal variability of PEVI, based on the Poisson-generalized Pareto (Poisson-GP) model, is investigated on weekly maxima observations available at 2.5 degree grids for 1940-2004 in South America. From 1965-2004, the PEVI shows increasing trends in few parts of the Amazon basin and the Brazilian highlands, north-west Venezuela including Caracas, north Argentina, Uruguay, Rio De Janeiro, Sao Paulo, Asuncion, and Cayenne. Catingas, few parts of the Brazilian highlands, Sao Paulo and Cayenne experience increasing number of consecutive 2- and 3-days extremes from 1965-2004. This dissertation also addresses the ability to detect the chaotic signal from a finite time series observation of hydrologic systems. Tests with simulated data demonstrate the presence of thresholds, in terms of noise to chaotic-signal and seasonality to chaotic-signal ratios, beyond which the set of currently available tools is not able to detect the chaotic component. Our results indicate that the decomposition of a simulated time series into the corresponding random, seasonal and chaotic components is possible from finite data. Real streamflow data from the Arkansas and Colorado rivers do not exhibit chaos. While a chaotic component can be extracted from the Arkansas data, such a component is either not present or can not be extracted from the Colorado data.

In 1975, H. Fujimoto generalized Nevanlinna's known results for meromorphic fonctions to the case of meromorphic mappings of Cn into PN(C). He proved that for two linearly nondegenerate meromorphic mappings f and g of C into PN(C). if they have the saine inverse images counted with multiplicities for 3N + 2 hyperplanes in general position in PN(C) then f = g. After that, this problem has been studied intensively by a number of mathematicans as H. Fujimoto, W. Stoll, L. Smiley, M. Ru, G. Dethloff - T. V. Tan, D. D. Thai - S. D. Quang, Chen-Yan and so on. Parallel to the development of Nevanlinna theory, the value distribution theory of the Gauss map of minimal surfaces immersed in Rm vas studied by many mathematicans as R. Osserman, S.S. Chern, F. Xavier, H. Fujimoto, S. J. Kao, M. Ru and many other mathematicans. In this thesis, we continuous studing some problems on these directions. The main goals of the thesis are followings. * Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) sharing 2N + 2 fixed hyperplanes.* Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) for moving targets, and a small set of identity.

Tegul s=σ+it yra kompleksinis kintamasis. Oilerio sandaugos yra apibrėžiamos pagal pirminius skaičius, taip pat yra reikalaujama, kad funkcija L(s) tenkintų papidomas sąlygas. Mes įrodome diskrečią ribinę teoremą tikimybinių matų silpno konvergavimo prasme kompleksinėje plokštumoje C Oilerio sandaugoms. / Let s=σ+it be a complex variable. The Euler products L(s) is defined by the prime number. If the function L(s) satisfies some additional hypotheses. In the Master work we prove the discrete limit theorem in the sense of weakly convergent probability measures for the Euler products on the complex plane.

Disertaciją sudaro mokslinių tyrimų medžiaga, kurie atlikti 2008 -2012 metais Vilniaus universitete Matematikos ir informatikos fakultete. Disertacijoje įrodomos naujos teoremos apie Lercho ir Selbergo dzeta funkcijų reikšmių pasiskirstymą, atliekami kompiuteriniai skaičiavimai matematine programa MATHEMATICA. Disertaciją sudaro įvadas, 3 skyriai, išvados ir literatūros sąrašas. Disertacijos rezultatai atspausdinti trijuose moksliniuose straipsniuose, Lietuvos ir užsienio žurnaluose, pristatyti Lietuvoje ir užsienyje vykusiose mokslinėse konferencijose bei katedros seminarų metu. Pirmajame skyriuje įrodinėjamos ribinės teoremos Lercho dzeta funkcijai. Praėjusio šimtmečio ketvirtame dešimtmetyje Selbergas įrodė, kad tinkamai normuotas Rymano dzeta funkcijos logaritmas ant kritinės tiesės turi standartinį normalųjį pasiskirstymą. Selbergo įrodymas rėmėsi Oilerio sandauga, kuria turi Rymano dzeta funkcija, bet bendru atveju jos neturi Lercho dzeta funkcija. Antrajame skyriuje įrodoma teorema apie Lercho transcendentinės funkcijos nulių įvertį vertikaliose kompleksinės plokštumos juostose bei atliekami kompiuteriniai nulių skaičiavimai srityje Re(s)>1 programa MATHEMATICA. Trečiajame skyriuje nagrinėjamos dviejų Selbergo dzeta funkcijų monotoniškumo savybės, kurios yra tiesiogiai susijusios su šių funkcijų nulių išsidėstymu kritinėje juostoje. Monotoniškumo savybės lyginamos su Rymano dzeta funkcijos monotoniškumo savybėmis ir nulių išsidėstymu, kuris yra viena didžiausių... [toliau žr. visą tekstą] / The doctoral dissertation contains the material of scientific investigations done in 2008-2012 in the Faculty of Mathematics and Informatics at Vilnius University. The dissertation includes new theorems for the value distribution of Lerch and Selberg zeta-functions and computer calculations performed using the computational software program MATHEMATICA. The dissertation consists of the introduction, 3 chapters, the conclusions and the references. The results of the thesis are published in three scientific articles in Lithuanian and foreign journals, reported in scientific conferences in Lithuania and abroad and at the seminars of the department. In the first chapter, the limit theorems for several cases of the Lerch zeta-functions are proved. In the 1940s, Selberg proved that suitably normalized logarithm of modulus of the Riemann zeta-function on the critical line has a standard normal distribution. Selberg's proof was based on the Euler product; however, in general, Lerch zeta-functions have no Euler product. In the second chapter, the theorem concerning the zero distribution of the Lerch transendent function is proved, and computer calculations of zeros in the region Re(s)>1 are performed using MATHEMATICA. In the third chapter, the monotonicity properties of Selberg zeta-functions are investigated. Monotonicity of these two functions is directly related to the location of zeros in the critical strip. The results are compared to the monotonicity... [to full text]

Tegul s yra kompleksinis kintamasis. Oilerio sandaugos apibrėžiamos pagal pirminius p skaičius. Funkcija L(s) turi tenkinti hipotezes. Magistro darbe, įrodome diskrečią ribinę teoremą silpno tikimybinių matų konvergavimo prasme Oilerio sandaugoms kompleksinėje plokštumoje. Gauta mato išreikštinė forma. / Let s be a complex variable. The Euler products is defined by the prime number p. The Function L(s) satisfies some additional hypoteses. In Master work, we prove the discrete limit theorem in the sense of weakly convergent probability measures for the Euler products on the complex plane. Then the probability measure weakly converges to the distribution of one explicitly given complex-valued random element as N-> infinity.

The doctoral dissertation contains the material of scientific investigations done in 2008-2012 in the Faculty of Mathematics and Informatics at Vilnius University. The dissertation includes new theorems for the value distribution of Lerch and Selberg zeta-functions and computer calculations performed using the computational software program MATHEMATICA. The dissertation consists of the introduction, 3 chapters, the conclusions and the references. The results of the thesis are published in three scientific articles in Lithuanian and foreign journals, reported in scientific conferences in Lithuania and abroad and at the seminars of the department. In the first chapter, the limit theorems for several cases of the Lerch zeta-functions are proved. In the 1940s, Selberg proved that suitably normalized logarithm of modulus of the Riemann zeta-function on the critical line has a standard normal distribution. Selberg's proof was based on the Euler product; however, in general, Lerch zeta-functions have no Euler product. In the second chapter, the theorem concerning the zero distribution of the Lerch transendent function is proved, and computer calculations of zeros in the region Re(s)>1 are performed using MATHEMATICA. In the third chapter, the monotonicity properties of Selberg zeta-functions are investigated. Monotonicity of these two functions is directly related to the location of zeros in the critical strip. The results are compared to the monotonicity... [to full text] / Disertaciją sudaro mokslinių tyrimų medžiaga, kurie atlikti 2008 -2012 metais Vilniaus universitete Matematikos ir informatikos fakultete. Disertacijoje įrodomos naujos teoremos apie Lercho ir Selbergo dzeta funkcijų reikšmių pasiskirstymą, atliekami kompiuteriniai skaičiavimai matematine programa MATHEMATICA. Disertaciją sudaro įvadas, 3 skyriai, išvados ir literatūros sąrašas. Disertacijos rezultatai atspausdinti trijuose moksliniuose straipsniuose, Lietuvos ir užsienio žurnaluose, pristatyti Lietuvoje ir užsienyje vykusiose mokslinėse konferencijose bei katedros seminarų metu. Pirmajame skyriuje įrodinėjamos ribinės teoremos Lercho dzeta funkcijai. Praėjusio šimtmečio ketvirtame dešimtmetyje Selbergas įrodė, kad tinkamai normuotas Rymano dzeta funkcijos logaritmas ant kritinės tiesės turi standartinį normalųjį pasiskirstymą. Selbergo įrodymas rėmėsi Oilerio sandauga, kuria turi Rymano dzeta funkcija, bet bendru atveju jos neturi Lercho dzeta funkcija. Antrajame skyriuje įrodoma teorema apie Lercho transcendentinės funkcijos nulių įvertį vertikaliose kompleksinės plokštumos juostose bei atliekami kompiuteriniai nulių skaičiavimai srityje Re(s)>1 programa MATHEMATICA. Trečiajame skyriuje nagrinėjamos dviejų Selbergo dzeta funkcijų monotoniškumo savybės, kurios yra tiesiogiai susijusios su šių funkcijų nulių išsidėstymu kritinėje juostoje. Monotoniškumo savybės lyginamos su Rymano dzeta funkcijos monotoniškumo savybėmis ir nulių išsidėstymu, kuris yra viena didžiausių... [toliau žr. visą tekstą]