Two families of kurtosis measures are defined as K1(b) = E[ab-|z|] and K2(b) = E[a(1 - |z|b)] where z denotes the standardized variable and a is a normalizing constant chosen such that the kurtosis is equal to 3 for normal distributions. K2(b) is an extension of Stavig's robust kurtosis. As with Pearson's measure of kurtosis β2 = E[z4], both measures are expected values of continuous functions of z that are even, convex or linear and strictly monotonic in ℜ- and in ℜ+. In contrast to β2, our proposed kurtosis measures give more importance to the central part of the distribution instead of the tails. Tests of normality based on these new measures are more sensitive with respect to the peak of the distribution. K1(b) and K2(b) satisfy Van Zwet's ordering and correlate highly with other kurtosis measures such as L-kurtosis and quantile kurtosis.

The aim of this study was to, on the basis of normalization and autonomy; investigate how staff working in group homes discusses about sexuality of people with an intellectual disability. Our study was based on ten semi-structured interviews of both care staff and heads of group homes to get responses from different levels within the same organization. The empirical material was analyzed through the theory of social constructivism, which focuses on how we construct the world through interaction and language, and the normalization principle whose goal is that all people with developmental disabilities should have the opportunity to live like all other people. We view these theories as useful to gain understanding of the questions in our study. The result of this study showed that the subject only comes up for discussion when problems arise, that the communication on the subject is inadequate and more discussion is requested. Further the result illustrated that staff strives for people with developmental disabilities to feel they have autonomy but this is also a challenge in their work.

Coming Through, a novel based on factual events, explores elements of the alternative sub-culture in Australia in the period between 1959 and 1980. Dual protagonists, Anna Martin and Jack Rose, personify aspects of the movement that would later be known as 'psychedelic romanticism.' The narrative follows Jack Rose's disenchantment with the prevailing social system and his efforts to achieve personal integration and his conflict with societal pressures to conform. Likewise, in a parallel narrative, it describes the events that surround Anna Martin's early institutionalisation and her attempt to achieve personal authenticity. When the protagonists finally encounter one another they find that a common and binding philosophy has drawn them together. The thesis looks at the prevailing social notions of'normality' at the time and the problems associated with alienation and the struggle to found alternative life styles in a society they deem to be repressive.

Darbe nagrinėjami taškiniai procesai (nehomogeninis Puasono procesas ir atstatymo procesas), randamos bendrosios sąlygos, kad būtų patenkintas lokalus asimptotinis normalumas. / The purpose of this work is to determine general conditions for local asymptotic normality to be assured.The point processes (renewal process and non-homogenous Poisson process) and their properties are examined in the first part of work. Then the conditions for the local asymptotic normality have been investigated. In the second part of work it is shown how these conditions are satisfied in the cases of the renewal process and non-homogenous Poisson process.

”Between normal and abnormal” is a qualitative literature study about adults with Aspergers syndrom. The study aims to understand how a person with Asperger syndrome understand himself. The study is built around two issues. These are; how does a person with Aspergers syndrom describe himself and how does the diagnos influence the self-image. The study interpreted four autobiographical books written by individuals with Asperger's syndrome based on a social constructive and social psychological approach. There is a risk that people who do not have the right or enough information about what an Asperger Diagnosis involves misunderstand the individual. This increases the risk that individuals with Asperger's syndrome may be devalued or get expectations of themselves that will be difficult to achieve. This may in turn have implications for self-esteem and self-perception. The results demonstrate that all writers feel that they are misunderstood, failed and different. The comparison is made with the "normal" and the feeling of being different gives a negative association. However, it also appears that when the diagnosis is obtained, there is a change in their understanding of the difficulties and life experiences they have. The feeling of being different gets a more positive association when their behavior becomes more legitimate, and there arises a sense of being part of the Asperger group which strengthens their self-esteem. Understanding themselves as deviant and odd change to a feeling of being normal though normal in a different way. This is also confirmed by other research (Larsson, 2007). The study also demonstrates that there is a dilemma between being the diagnos and being ones own person with ones own personality.

Student's t Distribution is introduced with background including comments on its robustness properties. The ad hoc procedure of pretesting data for normality is discussed in the light of current advice, and previous work into its effectiveness reviewed. The approach to the problem is outlined: √b1 for test statistic, the Gram-Charlier distribution for population, approximations using the Johnson system.

The purposes of the thesis were to review some of the existing methods for testing normality and to investigate the use of generated data combined with observed to test for normality. The approach to testing for normality is in contrast to the existing methods which are derived from observed data only. The test of normality proposed follows a characterization theorem by Bernstein (1941) and uses a test statistic D*, which is the average of the Hoeffding’s D-Statistic between linear combinations of the observed and generated data to test for normality. Overall, the proposed method showed considerable potential and achieved adequate power for many of the alternative distributions investigated. The simulation results revealed that the power of the test was comparable to some of the most commonly used methods of testing for normality. The test is performed with the use of a computer-based statistical package and in general takes a longer time to run than some of the existing methods of testing for normality.

<p> Several test statistics, which are known, can be used for testing for exponentiality. A new test statistic TE is proposed. TE is based on a censored sample and is similar to Tiku's T statistic for testing for normality. The distribution of TE tends to normality with increasing sample size. Besides, TE is easy to compute and is both origin and scale invariant. The power of TE for non-exponential distributions is comparable with Shapiro & Wilk statistic W-exponential. </p> / Thesis / Master of Science (MSc)

In order to make statistical inference, that is drawing conclusions from a sample to describe a population, it is crucial to know the correct distribution of the data. This paper focused on censored data from the normal distribution. The purpose of this paper was to answer whether we can test if data comes from a censored normal distribution. This by using normality tests and tests designed for censored data and investigate if we got correct size of these tests. This has been carried out with simulations in the program R for left censored data. The results indicated that with increasing censoring normality tests failed to accept normality in a sample. On the other hand the censoring tests met the requirements with increasing censoring level, which was the most important conclusion in this paper.

The study seeks to determine the degree of accumulation of Type II error rates, while violating the assumptions of normality, for different specified levels of power among sample means. The study employs a Monte Carlo simulation procedure with three different specified levels of power, methodologies, and population distributions. On the basis of the comparisons of actual and observed error rates, the following conclusions appear to be appropriate. 1. Under the strict criteria for evaluation of the hypotheses, Type II experimentwise error does accumulate at a rate that the probability of accepting at least one null hypothesis in a family of tests, when in theory all of the alternate hypotheses are true, is high, precluding valid tests at the beginning of the study. 2. The Dunn-Bonferroni procedure of setting the critical value based on the beta value per contrast did not significantly reduce the probability of committing a Type II error in a family of tests. 3. The use of an adequate sample size and orthogonal contrasts, or limiting the number of pairwise comparisons to the number of means, is the best method to control for the accumulation of Type II errors. 4. The accumulation of Type II error is irrespective of distributions.