ESTIMATION OF MEAN ON THE BASIS OF CONDITIONAL SIMPLE RANDOM SAMPLE

Estimation of the population mean in a finite and fixed population on the basis of the conditional simple random sampling design dependent on order statistics (quantiles) of an auxiliary variable is considered. Properties of the well-known Horvitz-Thompson and ratio type estimators as well as the sample mean are taken into account under the conditional simple random sampling designs. The considered examples of empirical analysis lead to the conclusion that under some additional conditions the proposed estimation strategies based on the conditional simple random sample are usually more accurate than the mean from the simple random sample drawn without replacement

O procedurze kart kontrolnych w przypadku, gdy zmienna diagnostyczna ma rozkład asymetryczny

The problem of statistical quality control is taken into account. A new proposition of control card construction is proposed. The problem is considered as testing statistical hypothesis on expected value of the variable understudy (diagnostic variable) under the assumption that the variable has skewed probability. The proposed test statisticis constructed on the rather well known following property that the covariance between sample variance and sample mean is proportional to the third central moment of a variable. This property is applied to construction of test statistic based on the regression estimator. The limit distribution of the test statistic is normal.W mniejszej pracy rozważano powszechnie używaną w statystycznej kontroli jakości procedurę kart kontrolnych lecz przy założeniu, że zmienna diagnostyczna ma niekoniecznie rozkład symetryczny. Analizowany problem sprowadzono do zagadnienia weryfikacji hipotezy o wartości oczekiwanej tej zmiennej diagnostycznej, przy czym zakłada się, że ta zmienna ma rozkład asymetryczny. Znaną własność występowania korelacji między średnią i wariancją z tej samej próby wykorzystano do konstrukcji sprawdzianu testu. Wykazano, że ten sprawdzian ma granicznie rozkład normalny. Przy spełnieniu pewnych dodatkowych warunków test wykorzystujący proponowany sprawdzian może mieć większą moc od testu, którego sprawdzianem jest zwykła średnia arytmetyczna z próby prostej

Estimation of Mode on the Basis of a Truncated Sample

The problem of estimation of the mode of a continuous distribution (unction is considered. The estimation of the mode based on estimators of the density function is well known, see e.g. Härdle (1991) and Parzen (1962). New parameters of the continuous distribution function will be defined: the quasi-mode and mean median. They are parameters of the appropriately truncated random variable. Next, the estimators of the mode, such as the sample quasi-mode or sample mean-median, are determined. These statistics are usually biased estimators of the mode. Well known “jackknife” procedure is adapted to estimate Their mean square error. The accuracy of the mode estimation is studied on the basis of computer simulation.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej nauk

Optimization of the break-even point for non-homogeneous products sales

Break-even point analysis is a classic management accounting tool. In the case of the sale of one product, the notion of the break-even point is well described in the literature, conceptually simple, and relatively easy to apply in business practice. However, when it comes to heterogeneous sales, consisting of various products, this problem is presented less frequently, and the methods used in this case exploit rather arbitrary and often ambiguous criteria. The aim of the article is to present and analyze alternative ways of determining break-even points for non-homogeneous sales based on econometric modeling methods. Production levels determined by the proposed methods meet the classical condition set for the break-even point, and in addition are optimal from the point of view of criteria used in the economic analysis. Three methods were presented: first – based on the classic criterion of profit maximization and linear programming, second – minimizing variable production costs and taking into account the scale effects on the production costs, and third – taking into account the random aspect of the business operations and maximizing the probability of profitability. According to the authors' knowledge, the proposed methods are original and are not known in the existing literature on the subject

Functional and bioinformatics analysis of two Campylobacter jejuni homologs of the thiol-disulfide oxidoreductase, DsbA.

BACKGROUND: Bacterial Dsb enzymes are involved in the oxidative folding of many proteins, through the formation of disulfide bonds between their cysteine residues. The Dsb protein network has been well characterized in cells of the model microorganism Escherichia coli. To gain insight into the functioning of the Dsb system in epsilon-Proteobacteria, where it plays an important role in the colonization process, we studied two homologs of the main Escherichia coli Dsb oxidase (EcDsbA) that are present in the cells of the enteric pathogen Campylobacter jejuni, the most frequently reported bacterial cause of human enteritis in the world. METHODS AND RESULTS: Phylogenetic analysis suggests the horizontal transfer of the epsilon-Proteobacterial DsbAs from a common ancestor to gamma-Proteobacteria, which then gave rise to the DsbL lineage. Phenotype and enzymatic assays suggest that the two C. jejuni DsbAs play different roles in bacterial cells and have divergent substrate spectra. CjDsbA1 is essential for the motility and autoagglutination phenotypes, while CjDsbA2 has no impact on those processes. CjDsbA1 plays a critical role in the oxidative folding that ensures the activity of alkaline phosphatase CjPhoX, whereas CjDsbA2 is crucial for the activity of arylsulfotransferase CjAstA, encoded within the dsbA2-dsbB-astA operon. CONCLUSIONS: Our results show that CjDsbA1 is the primary thiol-oxidoreductase affecting life processes associated with bacterial spread and host colonization, as well as ensuring the oxidative folding of particular protein substrates. In contrast, CjDsbA2 activity does not affect the same processes and so far its oxidative folding activity has been demonstrated for one substrate, arylsulfotransferase CjAstA. The results suggest the cooperation between CjDsbA2 and CjDsbB. In the case of the CjDsbA1, this cooperation is not exclusive and there is probably another protein to be identified in C. jejuni cells that acts to re-oxidize CjDsbA1. Altogether the data presented here constitute the considerable insight to the Epsilonproteobacterial Dsb systems, which have been poorly understood so far

Estymacja wartości przeciętnych w populacji na podstawie wektora średnich z próby grupowej

The research was supported by the grant number 1 H02B 015 10 from the Polish Scientific Research Committee.The estimation of a vector of mean values is being considered. The vector estimator consists of simple cluster sample means. It is assumod that a population of a fixed size is divided into mutually disjoint clusters each of the same size. The variance-covariance matrix of the vector estimator is derived. It is a function of a homogeneity matrix of multidimensional variable which describes within-cluster spread of the multidimensional variable under research. The accuracy of estimation is measured by means of standard deviations of particular sample cluster means as well as by means of the trace or the determinant or the maximal eigenvalue of the variance-covariance matrix of the vector estimator. The accuracy of the vector of simple sample cluster means is compared with the accuracy of the vector of the simple sample means. The accuracy of the vector of simple sample cluster means increases when the degree of within-cluster spread of the distribution of a multidimensional variable increases. Hence, the population should be divided into such clusters that the within-cluster spread is as large as possible.Zakłada się, że skończona i ustalona populacja jest podzielona na równoliczne i rozłączne grupy. Na podstawie prostej próby grupowej jest wyznaczany wektor średnich, który daje oceny wektora przeciętnych w populacji. Wyprowadzono macierz wariancji i kowariancji wektora wartości średnich z próby grupowej. Jest ona zależna od macierzy wewnątrzgrupowej jednorodności rozkładu wielowymiarowej zmiennej. Precyzja estymacji jest oceniana za pomocą wariancji poszczególnych średnich z próby grupowej, śladu, wyznacznika lub maksymalnej wartości własnej macierzy wariancji i kowariancji. Precyzja wektora średnich z próby grupowej jest porównywana z precyzją wektora średniej z próby prostej. Okazuje się, że wektor średnich z próby grupowej jest precyzyjniejszy od wektora przeciętnych z próby prostej, gdy stopień wewnątrzgrupowego zróżnicowania wartości zmiennych jest dostatecznie duży.Zadanie pt. Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Dekompozycja szeregów czasowych oparta na zmodyfikowanej metodzie Warda

The trend of time series can change its direction. It is assumed that the time interval is divided into subintervals where the trend is given as particular linear function. The problem is how to divide the observation of time series into disjoint and coherent groups where they have linear trend. That is why the problem of the scatter of multivariable observation was first considered. The degree of data spread is measured by means of a coefficient called a discriminant of multivariable observation. It is equal to the sum of volumes of the parallelotops spanned on multidimensional observations. On the basis of it the modifications of the well known generalized variance were introduced. Geometrical properties of those parameters were investigated. The obtained results are used to generalize well-known clustering methods of Ward. One of the advantages of the method is that it finds clusters of high linear dependent multivariate observations. Finally, the results are used to partition a time series into homogeneous groups where observations are close to linear trend. There is considered an example.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę