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EN
The most important factor for the success of a company in today’s competitive environment is to have clearly defined goals. Objectives define what a company strives for, what it wants to achieve, and what it wants to realize in its activities. Clearly defined goals are necessary to ensure the sustainability and effectiveness of a company’s operations and the successful achievement of its desired results. This paper proposes an expert method for determining the strategic goals of a company. The experts ranked 24 strategic goals in terms of importance, and variance and coefficient of variation were then used to determine the consistency of the experts. As a result, 15 important strategic goals were identified of the 24 goals of the assessed transport company.
EN
The aim of the paper is to identify a methodology capable of assessing shoreline changes through a geomatic approach based on the use of GIS (Geographic Information System) software. The paper describes a case study that reports the evolution of a coastline over a period of more than 100 years using medium and large-scale metric maps available in different periods. In fact, the coastlines were obtained from the source maps of the Italian Cadastre (dated 1890), from numerical cartography available on the coastline and acquired in different period at scales 1:5000 and 1:2000 and, more recently, from the Google Earth Pro platform. To analyse the evolution of the coastline a new procedure has been performed which is based on the use of GIS software, in particular a plugin called DSAS that allows the evaluation of the changes in the coastline and also obtains a statistical analysis of its evolution. The results showed the ease and applicability of the method in determining the evolution of the coastline and the strong erosion of a stretch of coastline with important socio-economic consequences and repercussions was highlighted in the analysed case study.
EN
Metallurgical slags are an object of the increasing interest in terms of the possibility of their utilization, especially as materials used in the construction and road building industries, in the foundry industry for refining and purifying liquid alloys, the production of abrasives for surface treatment of remanufactured machine parts, as mine backfill materials. Metallurgical slags, in order to be used in foundry processes, should be characterized by the stability of the chemical composition. This paper presents the results of statistical analysis calculations, in which using a specific group f samples, knowing their chemical composition, the mean value Ā, variance Ϭ2, standard deviation Ϭ and the classical coefficient of variation V were determined. The research and its results report the amount of variation in considered components of the slags.
4
Content available remote O estymacji wartości średniej napięcia sinusoidalnego
PL
W artykule oceniono dokładność wyników estymacji wartości średniej napięcia sinusoidalnego. W tym celu zastosowano estymator wartości średniej obliczany na podstawie próbek napięcia. Wyznaczono obciążenie, wariancję i błąd średniokwadratowy estymatora.
EN
The article evaluates the accuracy of the estimating results of the mean value of a sinusoidal voltage. For this purpose, a mean value estimator calculated from voltage samples has been used. The bias, the variance and the mean squared error of an estimator have been determined.
PL
Przedstawiono sposób wyznaczania estymatorów wartości i niepewności menzurandu niekonwencjonalną metodą maksymalizacji wielomianu stochastycznego (PMM) dla próbki danych pomiarowych pobranych z populacji modelowanej zmienną losową o rozkładzie niesymetrycznym. W metodzie PMM stosuje się statystykę wyższego rzędu i opis z użyciem momentów lub kumulantów. Wyznaczono wyrażenia analityczne dla estymatorów wartości i niepewności standardowej typu A menzurandu za pomocą wielomianu stopnia r = 2. Niepewność standardowa wartości menzurandu otrzymana metodą PPM zależy od skośności i kurtozy rozkładu. Jest ona mniejsza od średniej arytmetycznej wyznaczanej wg przewodnika GUM i bliższa wartości teoretycznej dla rozkładu populacji danych. Jeśli rozkład ten jest nieznany, to estymatory momentów i kumulantów wyznacza się z danych pomiarowych próbki. Sprawdzono skuteczność metody PMM dla kilku podstawowych rozkładów.
EN
The non-standard method for evaluating estimators of the value and uncertainty type A for measurement data sampled from asymmetrical distributed with a priori partial description (unknown PDF) is presented. This method of statistical estimation is based on the mathematical apparatus of stochastic polynomials maximization and uses the higher-order statistics (moment & cumulant description) of random variables. The analytical expressions for finding estimates and analyze their accuracy to the degree of the polynomial r = 2 are obtained. It is shown that the uncertainty of estimates received for polynomial is generally less than the uncertainty of estimates obtained based on the mean (arithmetic average) according international guide GUM. Reducing the uncertainty of measurement depends on the skewness and kurtosis. On the basis of the Monte Carlo method carried out statistical modelling. Their results confirm the effectiveness of the proposed approach.
EN
The drill ability is a fundamental factor for bit penetration rate (PR) in mining engineering. The ability to predict the performance of rock drills is important for drilling operations. Not a single parameter defines the drill ability of a rock. For this task, a considerable amount of fieldwork must be done to provide the necessary data i.e.: rock properties and drilling technologies. The main purpose of this research is to conduct an experimental study under varying rotation and pressures on the drilling bit for different geological formations. This paper presents a statistical analysis of process parameters of drilling in a phosphate mine in Jebel Onk, Tebessa, Algeria. Settings drilling parameters were determined by applying the design of experiments method. The level of importance of drilling parameters is determined by using analysis of variances. First, the teamwork determined the mathematical model for representative conditions of the phosphate mine of Jebel Onk. This mathematical model is a vital mathematical requirement for the operation engineers to deduce and determine the penetration rate according to the demands of work and to maximize the efficiency of the drilling machine and to minimize the bit wear in the abrasive layer.
PL
W artykule przedstawiono jednoczynnikową analizę wariancji prędkości statków na Zatoce Pomorskiej w kolejnych tygodniach stycznia i lutego 2017 roku. Zweryfikowano hipotezę o równości przeciętnych prędkości statków w poszczególnych tygodniach, sprawdzając najpierw założenia niezbędne do przeprowadzenia testu ANOVA. Do sprawdzenia normalności rozkładów wykorzystano testy Cramera von Misesa i Andersona-Darlinga, a do oceny jednorodności wariancji posłużył test Lavene’a.
EN
In this paper one-factor, fixed-effects completely randomized design of analysis of variance for vessel speed on the Pomeranian Bay has been presented. The hypothesis on the equality of the vessel speed means in nine weeks in January and February 2017 has been verified. To verify normality of distributions tests Cramer von Mises and Anderson-Darling have been used. To assess the equality of variances Levene’s test has been used.
EN
From first-order incremental ΣΔ converters to controlled-oscillator-based converters, many ADC architectures are based on the continuous-time integration of the input signal. However, the accuracy of such converters cannot be properly estimated without establishing the impact of noise. In fact, noise is also integrated, resulting in a random error that is added to the measured value. Since drifting phenomena may make simulations and practical measurements unable to ensure longterm reliability of the converters, a theoretical tool is required. This paper presents a solution to compute the standard deviation of the noise-generated error in continuous-time integrator-based ADCs, under the assumption that a previous measure is used to calibrate the system. In addition to produce a realistic case, this assumption allows to handle a theoretical issue that made the problem not properly solvable. The theory is developed, the equations are solved in the cases of pure white noise, pure flicker noise and low-pass filtered white noise, and the implementation issues implied by the provided formulas are addressed.
PL
Zastosowano metodę maksymalizacji wielomianu do syntezy adaptacyjnych algorytmów dla estymacji punktu zmiany wartości średniej oraz wariancji szeregu losowego w trybie a posteriori. Analiza i wyniki modelowania statystycznego wykazały, że uwzględniając parametry nie-gaussowskich danych statystycznych w oszacowaniu wielomianowym uzyskuje się istotny wzrost dokładności.
EN
An application of the maximization technique in the synthesis of polynomial adaptive algorithms for a posterior (retrospective) estimation of the change-point of the mean value or variance of random sequences is presented. Statistical simulation shows a significant increase in the accuracy of polynomial estimates, which is achieved by taking into account the non-Gaussian character of statistical data.
10
Content available Wartości resztowe w procesie regresji
PL
W artykule autor we wstępie argumentuje potrzebę przeprowadzenia weryfikacji opracowanego modelu regresji za pomocą analizy wartości resztowych. Na początku scharakteryzowano założenia analizy reszt, zwracając uwagę na własności tych reszt czyli: normalność, stałość wariancji i brak autokorelacji. Do analizy wzięto wyniki badań zapalników artyleryjskich typu MD-7. Scharakteryzowano własność wartości resztowych, która głosi, że reszty modelu mają rozkład normalny. Następnie omówiono sposób wyznaczania autokorelacji wartości resztowych, uwzględniając test Durbina-Watsona, który służy do weryfikacji współczynnika autokorelacji. Ze względu na obszerność artykułu nie analizowano metody mnożników Lagrange'a. Omówiono własność stałości wariancji wartości resztowych, czyli założenie homoscedastyczności składnika losowego. W tym celu przedstawiono wykresy rozrzutu reszt względem wartości przewidywanych. Zaprezentowano sposób określania obserwacji nietypowych w analizie procesu regresji. Przedstawiono graficzną postać interpretacji obserwacji odstających za pomocą wykresu rozrzutu reszt względem reszt usuniętych. Na końcu artykułu przedstawiono zwięzłe wnioski dotyczące wartości resztowych w procesie regresji.
EN
In the introduction of the article the author presents the need of verifying a developed regress model by using the analysis of residuum values. On the beginning the presumptions of the residuum analysis are characterized, paying the attention to properties of these residuum i.e.: normality, constancy of variance and lack of autocorrelation. Tests results of artillery fuses type MD-7 were taken to analysis. A property of residuum values showing that residuum of a model have a normal distribution was characterized. Then a way of determining the autocorrelation of residuum values was described, taking into account Durbin-Watson's test, which is used to verify the autocorrelation coefficient. Due to the extensiveness of the article, the method of Lagrange multipliers is not analyzed. A property of variance residuum values constancy i.e. presumption on homoscedasticity of random component is described. The residuum scatter diagrams in relation to forecast values are presented to prove it. A way defining atypical observations in the analysis of regress process was outlined. A graphic figure of interpretation for atypical observations by using residuum scatter diagram in relation to deleted residuum is discussed. Concise conclusions relating to the residuum values in the regress process are presented at the end of the article.
EN
Hydrological models are very useful for predictions in many ungauged basins across the world. There are many hydrological models available for discharge data gen-eration with different complexities and varied input parameter requirements. Studies have shown that models with many input parameters do not necessarily perform better than those with few input parameters. Basin morphometric parameters play significant roles in the conversion of rainfall to runoff and obtaining good estimates of these parameters for use in runoff models is sometime challenging as Inaccurate input into models can propagate errors and make the models to perform poorly. This study employs the method of principal component analysis to reduce the number of morphometric parameters required to run a runoff model without losing any major information. Parameters for five selected study basins in central Nigeria were measured and analysed. The result shows that three morphometric parameters (Fitness Ratio, Ruggedness Number and Watershed Eccentricity) can adequately represent other parameters as an input into a runoff model for the basins. This reduces significantly the time and effort needed to compute all the parameters which in actual fact may not improve the quality or efficiency of the runoff model.
EN
In this paper empirical formulas relating the speed to principal dimensions of aircraft carriers have been obtained through regression analysis of the data of 105 aircraft carriers. To reduce uncertainty as much as possible, aircraft carriers are classified into several different categories. In each category, regression analysis is separately performed such that a variety of regression (empirical) formulas have thus been obtained for possible use at the initial design stage of a carrier. The goodness of fit of these formulas is finally analyzed through variance analysis.
13
Content available remote Probabilistic properties of sinusoidal signal autocorrelation function
EN
The paper concerns issues of probabilistic properties of the sinusoidal signal autocorrelation function. An autocorrelation function can be viewed as a random variable with fixed probability density. In the paper, results of the research on parameters of such a variable are presented. On the basis of the probability density function, the mean, the mean-square and the variance of the random variable have been determined.
PL
Artykuł dotyczy problematyki probabilistycznych własności funkcji autokorelacji sygnału sinusoidalnego. Funkcja autokorelacji może być rozpatrywana jako zmienna losowa o ustalonej gęstości prawdopodobieństwa. W artykule przedstawiono wyniki badań dotyczące parametrów takiej zmiennej losowej. Na podstawie funkcji gęstości wyznaczono wartość oczekiwaną, średniokwadratową i wariancję zmiennej losowej.
14
Content available remote Some Decompositions of Matrix Variances
EN
When D is a density matrix and A1, A2 are self-adjoint operators, then the standard variance is a 2 × 2 matrix: VarD(A1, A2)i,j := TrDAiAj − (TrDAi)(TrDAj) (1 ≤ i, j ≤ 2). The main result in this work is that there are projections Pk such that D = Σk λk Pk with 0 < λk and Σk λk = 1 and VarD (A1, A2) = Σk λk VarPk (A1, A2). In a previous paper only the A1 = A2 case was included and the relevance is motivated by the paper [8].
EN
The paper is concerned with issues of the estimation of random variable distribution parameters by the Monte Carlo method. Such quantities can correspond to statistical parameters computed based on the data obtained in typical measurement situations. The subject of the research is the mean, the mean square and the variance of random variables with uniform, Gaussian, Student, Simpson, trapezoidal, exponential, gamma and arcsine distributions.
16
Content available remote Metoda pośredniego testowania wzajemnego skorelowania obserwacji losowych
PL
Zaproponowano i zbadano metodę testowania wzajemnego skorelowania losowych obserwacji bez bezpośredniego estymowania funkcji autokorelacji. Metoda polega na rozdzieleniu N zarejestrowanych obserwacji na k krótszych podserii o n obserwacji (N=n -k), estymowaniu i następnym porównywaniu wariancji wartości średnich tych serii z ich średnią wariancją. Ponieważ przy nieobecności skorelowania obserwacji stosunek estymatorów tych wariancji podlega rozkładowi F (Fishera-Snedecora) z liczbą stopni swobody k – 1 oraz N –k, dlatego odchylenie wartości stosunku estymatorów tych wariancji ponad dopuszczalną wartość Fk – 1, N – k (dla zadanego poziomu istotności α ) świadczy o wzajemnym skorelowaniu obserwacji. Przedstawiono wyniki badań skuteczności testowania metodą Monte-Carlo.
EN
A method of testing the autocorrelation of the random observations without direct estimation of their autocorrelation function was proposed and investigated. The proposed method consists in the separation of N registered observation into k shorter series containing of n observations (N = n -k), estimation and comparing the variance of the mean values of these series with an average of their variances. Because in the absence of the autocorrelation the ratio of the variance estimators is described by the F – distribution with the number of degrees of freedom k – 1 and N – k, therefore the deviation of this ratio from the critical value Fk – 1,N– k (for a given level of significance α) indicates the presence of the autocorrelation. Investigations of the effectiveness of the proposed test by Monte-Carlo method are presented.
17
Content available remote Variance as a Stopping Criterion for Genetic Algorithms with Elitist Model
EN
Genetic Algorithm (GA) has now become one of the leading mechanisms in providing solution to complex optimization problems. Although widely used, there are very few theoretical guidelines for determining when to stop the algorithm. This article establishes theoretically that the variance of the best fitness values obtained in the iterations can be considered as a measure to decide the termination criterion of a GA with elitist model (EGA). The criterion automatically takes into account the inherent characteristics of the objective function. Implementation issues of the proposed stopping criterion are explained. Its difference with some other stopping criteria is also critically analyzed.
18
EN
In most studies of nest-site selection the data of habitat parameters are treated with analysis of variance. A basic assumption of this test is the homogeneity of variance. Here, we show that the nest-site selection process leads to lower variance of the selected parameters than in the case of random points which generally describe the available average characteristics of the environment. Thus, the variance should be accounted for in studies on nest-site selection and it should be treated not as a problem (as it is usually done), but as a source of additional important information on the selection process. Comparison only of mean values often does not lead to significant differences between nest site parameters and random points which may result from a small effect size (when animals select features similar to the general mean of available characteristics). Deeper insight into variance of the site parameters may elicit important results. We illustrate this issue with real data on nest site (islets and shores of water reservoirs) selection in the Common Gull Larus canus. Four (islet's area, vegetation height on islets, vegetation cover on shore and distance to nearest shrub or tree on shore) from eight parameters were favored by the birds and, as predicted, their variance values were lower than of those not selected (vegetation cover on islets, distance of the islets to shoreline, vegetation height on shore and distance to water).
19
Content available Probabilistic characterization of strong convexity
EN
Strong convexity is considered for real functions defined on a real interval. Probabilistic characterization is given and its geometrical sense is explained. Using this characterization some inequalities of Jensen-type are obtained.
PL
W pracy przedstawiono wyniki badań propagacji wiązki światła lasera w śladzie aerodynamicznym wybranych obiektów. Zaobserwowano zależność między parametrami wiązki światła a kształtem modelowych obiektów. Do analizy wybrano rozkład amplitud natężenia światła, który przybliżono rozkładem gaussowskim. Parametry tego rozkładu mogą być przydatne do oszacowania wybranych parametrów śladu aerodynamicznego.
EN
The work presents some experimental examinations of the laser beam propagation in the aerodynamic wake of selected objects (obstacles). Large differences between laser light intensity for used objects were observed. Gaussian distribution (median, variance) for the light intensity was analyzed.
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