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The environment is everything around us. The environment provides fresh air, clean water and productive fertile soil for the manufacture of food etc., But in the current global scenario, it has been observed that human activities are continuously and constantly impacting our mother nature in a negative way. As we navigate the complexities of the 21st century, it becomes increasingly evident that our actions today profoundly impact the world we will inhabit tomorrow. In the 21st century our environment is facing a lot of problems like climate change, depletion of ozone layer, acid rain, population explosion, loss of biodiversity due to over exploitation of nature and natural resources. Therefore, there is an urgent need and it is high time to rescue our environment thereby to maintain a harmonious relationship between man and nature in a sustainable way. In the pursuit of progress and prosperity, humanity has often overlooked the critical importance of environmental sustainability. This book, "Sustainable Development in 21st Century through Clean Environment," explores the nexus between sustainable development and environmental preservation. Our collective challenge lies in fostering development that uplifts communities without compromising the integrity of these ecosystems upon which all life depends. Through a multidisciplinary approach, this book seeks to unravel the multifaceted dimensions of sustainable development. The various chapters included in this book are from different areas of environment on the current issues of environmental challenges and possible sustainable ways to overcome those issues. We sincerely hope that this book will be a great help and support to all the students, teachers, researchers and other environmental activists who wants to do some meaningful contributions towards the environment. We would also like to express our heartfelt gratitude to our publisher Mrs. Rajani Adam for her immense love and moral support and timely help in bringin

The environment is everything around us. The environment provides fresh air, clean water and productive fertile soil for the manufacture of food etc., But in the current global scenario, it has been observed that human activities are continuously and constantly impacting our mother nature in a negative way. As we navigate the complexities of the 21st century, it becomes increasingly evident that our actions today profoundly impact the world we will inhabit tomorrow. In the 21st century our environment is facing a lot of problems like climate change, depletion of ozone layer, acid rain, population explosion, loss of biodiversity due to over exploitation of nature and natural resources. Therefore, there is an urgent need and it is high time to rescue our environment thereby to maintain a harmonious relationship between man and nature in a sustainable way. In the pursuit of progress and prosperity, humanity has often overlooked the critical importance of environmental sustainability. This book, "Sustainable Development in 21st Century through Clean Environment," explores the nexus between sustainable development and environmental preservation. Our collective challenge lies in fostering development that uplifts communities without compromising the integrity of these ecosystems upon which all life depends. Through a multidisciplinary approach, this book seeks to unravel the multifaceted dimensions of sustainable development. The various chapters included in this book are from different areas of environment on the current issues of environmental challenges and possible sustainable ways to overcome those issues. We sincerely hope that this book will be a great help and support to all the students, teachers, researchers and other environmental activists who wants to do some meaningful contributions towards the environment. We would also like to express our heartfelt gratitude to our publisher Mrs. Rajani Adam for her immense love and moral support and timely help in bringin

The environment is everything around us. The environment provides fresh air, clean water and productive fertile soil for the manufacture of food etc., But in the current global scenario, it has been observed that human activities are continuously and constantly impacting our mother nature in a negative way. As we navigate the complexities of the 21st century, it becomes increasingly evident that our actions today profoundly impact the world we will inhabit tomorrow. In the 21st century our environment is facing a lot of problems like climate change, depletion of ozone layer, acid rain, population explosion, loss of biodiversity due to over exploitation of nature and natural resources. Therefore, there is an urgent need and it is high time to rescue our environment thereby to maintain a harmonious relationship between man and nature in a sustainable way. In the pursuit of progress and prosperity, humanity has often overlooked the critical importance of environmental sustainability. This book, "Sustainable Development in 21st Century through Clean Environment," explores the nexus between sustainable development and environmental preservation. Our collective challenge lies in fostering development that uplifts communities without compromising the integrity of these ecosystems upon which all life depends. Through a multidisciplinary approach, this book seeks to unravel the multifaceted dimensions of sustainable development. The various chapters included in this book are from different areas of environment on the current issues of environmental challenges and possible sustainable ways to overcome those issues. We sincerely hope that this book will be a great help and support to all the students, teachers, researchers and other environmental activists who wants to do some meaningful contributions towards the environment. We would also like to express our heartfelt gratitude to our publisher Mrs. Rajani Adam for her immense love and moral support and timely help in bringin

The sudden appearance of portolan charts, realistic nautical charts of the Mediterranean and Black Sea, in the last quarter of the thirteenth century, is considered to be one of the most significant events in the history of cartography. Using analysis techniques available in geodesy, Roel Nicolai showed in dissertation that these charts are mosaics of regional charts that are considerably more accurate than had been assumed earlier. The good agreement of these regional charts with the Mercator map projection is even more remarkable. Map projections were unknown in the Middle Ages and the Mercator projection was developed some three centuries after the appearance of the oldest extant portolan chart. Therefore, virtually unanimous agreement exists among historians of cartography that its map projection must be coincidental. In this article, however, Nicolai shows, using probability calculus, that it is very unlikely that the map projection emerged as an unintentional by-product of the charts’ construction.

The sudden appearance of portolan charts, realistic nautical charts of the Mediterranean and Black Sea, at the end of the thirteenth century is one of the most significant events in the history of cartography. By using geodetic and statistical analysis techniques, these charts are shown to be mosaics of regional charts that are considerably more accurate than has been assumed. Their accuracy exceeds medieval mapping capabilities. These regional charts show a remarkably good agreement with the Mercator map projection. It is demonstrated that it is very unlikely that this map projection is an unintentional by-product of the charts’ putative medieval construction, as is widely believed. While the physical charts are without doubt medieval, the possibility is eliminated that the charts are original products of a medieval Mediterranean nautical culture, which until now they have been widely believed to be. Their true origin must lie considerably further back in time.

Material de enseñanza para el aprendizaje del Diseño y Análisis de ANOVA multifactorial con cualquier tipo de factores (ortogonales y/o anidados, fijos y/o aleatorios). El aprendizaje de estas técnicas permitirá al alumnado diseñar experimentos ad hoc, optimizando el diseño del experimento teniendo en cuenta la optimización del esfuerzo y la mejora de la sensibilidad de ANOVA.

ANOVA multifactorial desde cero. Empezando con ANOVA de un factor, para qué sirve, cómo funciona por dentro, cómo se interpretan sus resultados. Alternativas no paramétricas. Inclusión de más factores. Diseños multifactoriales con factores Ortogonales. Interpretación de las interacciones, características de diseños ortogonales. Diseños con factores anidados. Características, cómo funciona, para qué sirve. Pseudo-replicación. Variabilidades a distintas escalas. Diseños multifactoriales mixtos o generalizados, ad-hoc. Método para revisar en la tabla de ANOVA los Grados de Libertad, estimadores de los cuadrados medios, denominadores de F. Optimización de diseños experimentales pensando en el análisis con ANOVA. Estrategias de diseño y de análisis.

ANOVA multifactorial desde cero. Empezando con ANOVA de un factor, para qué sirve, cómo funciona por dentro, cómo se interpretan sus resultados. Alternativas no paramétricas. Inclusión de más factores. Diseños multifactoriales con factores Ortogonales. Interpretación de las interacciones, características de diseños ortogonales. Diseños con factores anidados. Características, cómo funciona, para qué sirve. Pseudo-replicación. Variabilidades a distintas escalas. Diseños multifactoriales mixtos o generalizados, ad-hoc. Método para revisar en la tabla de ANOVA los Grados de Libertad, estimadores de los cuadrados medios, denominadores de F. Optimización de diseños experimentales pensando en el análisis con ANOVA. Estrategias de diseño y de análisis.

Material de enseñanza para el aprendizaje del Diseño y Análisis de ANOVA multifactorial con cualquier tipo de factores (ortogonales y/o anidados, fijos y/o aleatorios). El aprendizaje de estas técnicas permitirá al alumnado diseñar experimentos ad hoc, optimizando el diseño del experimento teniendo en cuenta la optimización del esfuerzo y la mejora de la sensibilidad de ANOVA.

One of most challenging research elements of medieval Mediterranean porto-lan charts is the matter of their elusive origin. This does not concern the origin of the surviving physical charts, but the origin of their geometrical information content, consisting primarily of the coastal outlines. Particularly challenging are the charts’ evident accuracy and their good agreement with a Mercator(-like) map projection. Key questions are how these charts were constructed and on the basis of what measurement data. While questions regarding the medieval usage of the charts, the economic aspects of chart construction and their fabrication process clearly fall in the domain of the historian, those concerning the construc-tion technique, accuracy and correspondence with a map projection have a very considerable geodetic component. It is my contention that geodetic aspects have not been given sufficient attention in the research into the origin of portolan charts. The almost complete absence of his-torical evidence regarding the charts’ origin requires the researcher to tread carefully and pay adequate attention to the methodological aspects of his or her research. I will discuss several examples where the eagerness to come forward with viable explanations has enticed researchers to step off the narrow path prescribed by the scientific method. Geodetic analysis enables the testing of hypotheses related to the geodetic aspects of portolan charts (construction, accuracy and map projection) with more scientific rigour than would be achievable without such tech-niques. The key questions regarding the origin of the charts can, in my opinion, only be answered with some hope of success by a fruitful synthesis of history, geodesy and cartography. Research-ers from the humanities are faced with a particular challenge to get an adequate understanding of geodetic, mathematical and statistical analysis techniques, in order to be able to understand the results such techniques may yield. Part

In two-armed trials with clustered observations the arms may differ in terms of (i) the intraclass correlation, (ii) the outcome variance, (iii) the average cluster size, and (iv) the number of clusters. For a linear mixed model analysis of the treatment effect, this paper examines the expected efficiency loss due to varying cluster sizes based upon the asymptotic relative efficiency of varying versus constant cluster sizes. Simple, but nearly cost-optimal, correction factors are derived for the numbers of clusters to repair this efficiency loss. In an extensive Monte Carlo simulation, the accuracy of the asymptotic relative efficiency and its Taylor approximation are examined for small sample sizes. Practical guidelines are derived to correct the numbers of clusters calculated under constant cluster sizes (within each treatment) when planning a study. Because of the variety of simulation conditions, these guidelines can be considered conservative but safe in many realistic situations. Copyright © 2016 John Wiley & Sons, Ltd.

In two-armed trials with clustered observations the arms may differ in terms of (i) the intraclass correlation, (ii) the outcome variance, (iii) the average cluster size, and (iv) the number of clusters. For a linear mixed model analysis of the treatment effect, this paper examines the expected efficiency loss due to varying cluster sizes based upon the asymptotic relative efficiency of varying versus constant cluster sizes. Simple, but nearly cost-optimal, correction factors are derived for the numbers of clusters to repair this efficiency loss. In an extensive Monte Carlo simulation, the accuracy of the asymptotic relative efficiency and its Taylor approximation are examined for small sample sizes. Practical guidelines are derived to correct the numbers of clusters calculated under constant cluster sizes (within each treatment) when planning a study. Because of the variety of simulation conditions, these guidelines can be considered conservative but safe in many realistic situations. Copyright © 2016 John Wiley & Sons, Ltd.

I study the equivalence between the Likelihood Ratio Test (LRT), Restricted Likelihood Ratio Test (RLRT) and the F-test when testing variance components within the class of generalized split-plot (GSP) models. In this work, I derive explicit expressions for both the maximum likelihood estimates (MLEs) and restricted maximum likelihood estimates (RMLEs) for the variance components of the GSP model and show the equivalence between the F-test, the LRT or the F-test and the RLRT when the level of the test, $\\alpha$, is less or equal to one minus the probability, $p$, that the LRT or the RLRT statistic is zero. However, when $\\alpha> 1-p$, I show that the F-test has a larger power than either the LRT or RLRT. Further, we derive the statistical distribution of these tests under both the null and alternative hypotheses $H_0$ and $H_1$ where $H_0$ is the hypothesis that the whole plot variance is zero. To establish the power inequality for the case $\\alpha> 1-p$, I developed a new stochastic inequality involving a class of distributions that includes, for example, the F and Gamma distributions. I call random variables (r.v.s.) that inherit this inequality to be quantile-stochastic. The stochastic representation of the new inequality involves $\\alpha, p\\in (0,1)$ such that if $p>\\alpha$ and $k>1$ with $W$ being a random variable with an $F(\ u_1,\ u_2)$ or $Gamma(\ au,\ heta)$ distribution then it's always true that \\[ \\frac{1}{p}P\\left(W<\\frac{W_p}{k}\\right)>\\frac{1}{\\alpha}P\\left(W<\\frac{W_{\\alpha}}{k}\\right), \\] where $\\gamma=P(W

I study the equivalence between the Likelihood Ratio Test (LRT), Restricted Likelihood Ratio Test (RLRT) and the F-test when testing variance components within the class of generalized split-plot (GSP) models. In this work, I derive explicit expressions for both the maximum likelihood estimates (MLEs) and restricted maximum likelihood estimates (RMLEs) for the variance components of the GSP model and show the equivalence between the F-test, the LRT or the F-test and the RLRT when the level of the test, $\\alpha$, is less or equal to one minus the probability, $p$, that the LRT or the RLRT statistic is zero. However, when $\\alpha> 1-p$, I show that the F-test has a larger power than either the LRT or RLRT. Further, we derive the statistical distribution of these tests under both the null and alternative hypotheses $H_0$ and $H_1$ where $H_0$ is the hypothesis that the whole plot variance is zero. To establish the power inequality for the case $\\alpha> 1-p$, I developed a new stochastic inequality involving a class of distributions that includes, for example, the F and Gamma distributions. I call random variables (r.v.s.) that inherit this inequality to be quantile-stochastic. The stochastic representation of the new inequality involves $\\alpha, p\\in (0,1)$ such that if $p>\\alpha$ and $k>1$ with $W$ being a random variable with an $F(\ u_1,\ u_2)$ or $Gamma(\ au,\ heta)$ distribution then it's always true that \\[ \\frac{1}{p}P\\left(W<\\frac{W_p}{k}\\right)>\\frac{1}{\\alpha}P\\left(W<\\frac{W_{\\alpha}}{k}\\right), \\] where $\\gamma=P(W

This paper discusses the possibility of applying the F-test and double t-test in problems related to the identification of number of radioactive isotopes in a contaminated area by using only counters for radiation detection. The descriptions of the F-test and the double t-test are given along with the corresponding tabular values that enable their implementation. Finally, the experiment is presented via two radioactive samples. The results of the experiment were treated in the manner proposed in the paper and satisfactory results were obtained.

This paper discusses the possibility of applying the F-test and double t-test in problems related to the identification of number of radioactive isotopes in a contaminated area by using only counters for radiation detection. The descriptions of the F-test and the double t-test are given along with the corresponding tabular values that enable their implementation. Finally, the experiment is presented via two radioactive samples. The results of the experiment were treated in the manner proposed in the paper and satisfactory results were obtained.

As a result of research on the non-noble metal-based composite electrocatalysts for the hydrogen evolution reaction (HER), the Ni-MoO2 composite coating was produced by electrodeposition from an NH4Cl and NiCl2 containing solution with suspended MoO2 powder particles, exhibiting almost the identical activity for the HER as the commercial cathode in conditions of industrial application and satisfactory mechanical stability. In this work, investigations were extended to the kinetics and mechanism of the HER on the Ni-MoO2 electrode in 8 M NaOH solution at 30 degrees C. The steady-state polarization curve for the HER was characterized by only one Tafel slope of -122 mV/dec. Kinetic parameters for the HER, as well as a contribution of surface roughness to the catalytic activity, were evaluated using an electrochemical impedance spectroscopy (EIS) technique. On the basis of the presented theoretical model for the faradaic impedance of the HER, the rate constants of the individual steps were determined by simulating both polarization and EIS experimental data. It was found that the reaction equally proceeds via the Volmer-Heyrovsky and Volmer-Tafel routes at lower overpotentials, while at higher overpotentials the Volmer-Heyrovsky pathway dominates the process with the Heyrovsky step being the rate determining step (rds). A comparison of intrinsic activities of the Ni-MoO2 composite and a flat Ni electrode proved that the combination of Ni and MoO2 produced a true catalytic effect for the HER.

As a result of research on the non-noble metal-based composite electrocatalysts for the hydrogen evolution reaction (HER), the Ni-MoO2 composite coating was produced by electrodeposition from an NH4Cl and NiCl2 containing solution with suspended MoO2 powder particles, exhibiting almost the identical activity for the HER as the commercial cathode in conditions of industrial application and satisfactory mechanical stability. In this work, investigations were extended to the kinetics and mechanism of the HER on the Ni-MoO2 electrode in 8 M NaOH solution at 30 degrees C. The steady-state polarization curve for the HER was characterized by only one Tafel slope of -122 mV/dec. Kinetic parameters for the HER, as well as a contribution of surface roughness to the catalytic activity, were evaluated using an electrochemical impedance spectroscopy (EIS) technique. On the basis of the presented theoretical model for the faradaic impedance of the HER, the rate constants of the individual steps were determined by simulating both polarization and EIS experimental data. It was found that the reaction equally proceeds via the Volmer-Heyrovsky and Volmer-Tafel routes at lower overpotentials, while at higher overpotentials the Volmer-Heyrovsky pathway dominates the process with the Heyrovsky step being the rate determining step (rds). A comparison of intrinsic activities of the Ni-MoO2 composite and a flat Ni electrode proved that the combination of Ni and MoO2 produced a true catalytic effect for the HER.

A modification of the ANOVA-PCA method, proposed by Harrington et al. to identify significant factors and interactions in an experimental design, is presented in this article. The modified method uses the idea of multiple table analysis, and looks for the common dimensions underlying the different data tables, or data blocks, generated by the "ANOVA-step" of the ANOVA-PCA method, in order to identify the significant factors. In this paper, the "Common Component and Specific Weights Analysis" method is used to analyse the calculated multi-block data set. This new method, called AComDim, was compared to the standard ANOVA-PCA method, by analysing four real data sets. Parameters computed during the AComDim procedure enable the computation of F-values to check whether the variability of each original data block is significantly greater than that of the noise.

公営事業民営化政策の主たる経済的目的は、民営化により対象事業の生産性の上昇を図ることである。本論文は、沖縄電力の完全民営化（1988年）を対象に、「生産性の上昇」という当初の政策目的が果たして民営化によって達成されたかどうかを、計量経済学および統計学の手法を用いて検証したものである。

Tato práce se zabývá problematikou zavedením vybraných statistický metod do firmy Jo-nal, spol. s r. o., které vedou k lepší informovanosti kompetentních osob. Podkladem pro tyto metody slouží ekonomické údaje jak z finančního, tak i z manažerského účetnictví. Vybrané ekonomické údaje jsou analyzovány pomocí výpočtů v tabulkovém procesoru Microsoft Excel a trial verzi programu STATGRAPHICS Centurion XV., This Bachelor thesis deals with implementation of selected statistical methods for Jonal Ltd. Selected statistical methods lead to better awareness of competent persons. Sources for these methods are gathered from economical data of finance and management accoun-ting. Selected commercial data are analyzed by means of calculations in spreadsheet pro-cessor Microsoft Excel and trial vision of STATGRAPHICS Centurion XV., Ústav informatiky a statistiky, obhájeno

A new empirical formula for the absorption of sound in seawater is derived. The starting point of this investigation is the formula proposed by Ainslie and McColm for attenuation due to the boron and magnesium relaxations. Constants in the expression are treated as parameters to be determined. Since this is a nonlinear inverse problem, a global search is used to find the parameter setting that yields the best fit to in situ absorption measurements. The obtained formula is simpler than and at least as accurate as the widely used absorption formula of Francois and Garrison., Text in English. Abstracts in English and Dutch. The original document contains color images. All DTIC reproductions will be in black and white.

We discuss the use of bootstrap methodology in hypothesis testing, focusing on the classical F-test for linear hypotheses in the linear model. A modification of the F-statistics which allows for resampling under the null hypothesis is proposed. This approach is specifically considered in the one-way analysis of variance model. A simulation study illustrating the behaviour of our proposal is presented., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací., Classical linear regression model and the respective tests are based on an assumption of normally distributed response variables and on an assumption of variance equality. If the normality assumption is not fulfilled, then the response variables are usually transformed. In the first part of this work variance stabilising transformations are discussed. Great deal of attention is given to random variables of Poisson and negative binomial distribution, for which generalised variance stabilising transformations with addition constants in their arguments are studied. Optimal values of the constants for the generalised transformations are determined. The second part aims to provide a comparison of the transformations introduced in the first part and some other commonly used transformations. The comparison is done within the ANOVA framework by testing the hypothesis of equality of expectations among p random samples via F test. The properties of the distribution of the F test under the assumptions of equal and unequal variances are studied. Finally a comparison of the power functions of the F test applied to p random samples from Poisson distribution transformed via square root, logarithmic and Yeo-Johnson transformation, and to p random sample of negative binomial distribution transformed via argument of hyperbolic sine, logarithmic and the Yeo-Johnson transformation is carried out theoretically and by simulations.

Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací., Classical linear regression model and the respective tests are based on an assumption of normally distributed response variables and on an assumption of variance equality. If the normality assumption is not fulfilled, then the response variables are usually transformed. In the first part of this work variance stabilising transformations are discussed. Great deal of attention is given to random variables of Poisson and negative binomial distribution, for which generalised variance stabilising transformations with addition constants in their arguments are studied. Optimal values of the constants for the generalised transformations are determined. The second part aims to provide a comparison of the transformations introduced in the first part and some other commonly used transformations. The comparison is done within the ANOVA framework by testing the hypothesis of equality of expectations among p random samples via F test. The properties of the distribution of the F test under the assumptions of equal and unequal variances are studied. Finally a comparison of the power functions of the F test applied to p random samples from Poisson distribution transformed via square root, logarithmic and Yeo-Johnson transformation, and to p random sample of negative binomial distribution transformed via argument of hyperbolic sine, logarithmic and the Yeo-Johnson transformation is carried out theoretically and by simulations.

Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací., Classical linear regression model and the respective tests are based on an assumption of normally distributed response variables and on an assumption of variance equality. If the normality assumption is not fulfilled, then the response variables are usually transformed. In the first part of this work variance stabilising transformations are discussed. Great deal of attention is given to random variables of Poisson and negative binomial distribution, for which generalised variance stabilising transformations with addition constants in their arguments are studied. Optimal values of the constants for the generalised transformations are determined. The second part aims to provide a comparison of the transformations introduced in the first part and some other commonly used transformations. The comparison is done within the ANOVA framework by testing the hypothesis of equality of expectations among p random samples via F test. The properties of the distribution of the F test under the assumptions of equal and unequal variances are studied. Finally a comparison of the power functions of the F test applied to p random samples from Poisson distribution transformed via square root, logarithmic and Yeo-Johnson transformation, and to p random sample of negative binomial distribution transformed via argument of hyperbolic sine, logarithmic and the Yeo-Johnson transformation is carried out theoretically and by simulations.

Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací., Classical linear regression model and the respective tests are based on an assumption of normally distributed response variables and on an assumption of variance equality. If the normality assumption is not fulfilled, then the response variables are usually transformed. In the first part of this work variance stabilising transformations are discussed. Great deal of attention is given to random variables of Poisson and negative binomial distribution, for which generalised variance stabilising transformations with addition constants in their arguments are studied. Optimal values of the constants for the generalised transformations are determined. The second part aims to provide a comparison of the transformations introduced in the first part and some other commonly used transformations. The comparison is done within the ANOVA framework by testing the hypothesis of equality of expectations among p random samples via F test. The properties of the distribution of the F test under the assumptions of equal and unequal variances are studied. Finally a comparison of the power functions of the F test applied to p random samples from Poisson distribution transformed via square root, logarithmic and Yeo-Johnson transformation, and to p random sample of negative binomial distribution transformed via argument of hyperbolic sine, logarithmic and the Yeo-Johnson transformation is carried out theoretically and by simulations.

Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací., Classical linear regression model and the respective tests are based on an assumption of normally distributed response variables and on an assumption of variance equality. If the normality assumption is not fulfilled, then the response variables are usually transformed. In the first part of this work variance stabilising transformations are discussed. Great deal of attention is given to random variables of Poisson and negative binomial distribution, for which generalised variance stabilising transformations with addition constants in their arguments are studied. Optimal values of the constants for the generalised transformations are determined. The second part aims to provide a comparison of the transformations introduced in the first part and some other commonly used transformations. The comparison is done within the ANOVA framework by testing the hypothesis of equality of expectations among p random samples via F test. The properties of the distribution of the F test under the assumptions of equal and unequal variances are studied. Finally a comparison of the power functions of the F test applied to p random samples from Poisson distribution transformed via square root, logarithmic and Yeo-Johnson transformation, and to p random sample of negative binomial distribution transformed via argument of hyperbolic sine, logarithmic and the Yeo-Johnson transformation is carried out theoretically and by simulations.

Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací., Classical linear regression model and the respective tests are based on an assumption of normally distributed response variables and on an assumption of variance equality. If the normality assumption is not fulfilled, then the response variables are usually transformed. In the first part of this work variance stabilising transformations are discussed. Great deal of attention is given to random variables of Poisson and negative binomial distribution, for which generalised variance stabilising transformations with addition constants in their arguments are studied. Optimal values of the constants for the generalised transformations are determined. The second part aims to provide a comparison of the transformations introduced in the first part and some other commonly used transformations. The comparison is done within the ANOVA framework by testing the hypothesis of equality of expectations among p random samples via F test. The properties of the distribution of the F test under the assumptions of equal and unequal variances are studied. Finally a comparison of the power functions of the F test applied to p random samples from Poisson distribution transformed via square root, logarithmic and Yeo-Johnson transformation, and to p random sample of negative binomial distribution transformed via argument of hyperbolic sine, logarithmic and the Yeo-Johnson transformation is carried out theoretically and by simulations.

697, This study conducted an analysis of the SCDOT HMA specification. A Research Steering Committee provided oversight, of the process. The research process included extensive statistical analyses of test data supplied by SCDOT., A total of 2,789 AC tests, 2,234 AV tests, and 2,230 VMA tests were provided from 20 different projects, with some, projects having multiple Mix Types and JMFs involved. A total of 2,010 density test results also were provided from 15, of the 20 projects. Relatively small amounts of data from certain Courses and Mix Types limited analyses only to, Surface Type A and Surface Type B mixes., The analyses led to a recommendation that SCDOT switch to using the differences from the AC, AV, and VMA target, values rather than the actual AC, AV, and VMA values. This will allow the possibility of combining test results from, more than 1 JMF in the Lot payment decision., In addition, SCDOT verification test results were provided from 16 of the 20 projects. These data consisted of 487 AC, and 452 AV and VMA test results from SCDOT. In addition, the data set included 411 AC, and 387 AV and VMA, Contractor verification test results. These data were analyzed to evaluate current SCDOT verification procedures and, issues concerning them were presented and discussed., Power curves were developed for various sample sizes for the F-test, the two-sample t-test, and the paired-sample t-test, to allow SCDOT to evaluate the risks associated with their current verification procedures as well as any possible, changes to the current procedures.