locating a changed segment in a sequence of bernoulli variables the theory underlying inferences about a single change point in a sequence of independent bernoulli variables is extended to the two change points problem where the distance between the two change points is known namely a changed segment both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations the distribution of the maximum likelihood estimator of the location of the changed segment is derived

detecting a shift in location some robust tests abstract the test statistic w suggested by hawkins 1977 and worsley 1979 for testing a sequence of observations for a shift in location is sensitive to the assumption that the distribution of the population being sampled is normal a modification of this statistic is proposed which is robust against heavy tailed distributions we also study the performance of several alternative testing procedures by means of a simulation experiment the farley hinich test 1975 and the homogeneity test discussed in brown durbin and evans 1975 perform well in the simulation experiment against heavy tailed distributions some applications to economic data are also discussed in the paper

multiple runs distributions recurrences and critical values abstract most traditional applications of runs tests have entailed bivariate runs distributions extensions to more general runs tests for randomness have been hindered by the lack of exact critical values for distributions with more than two kinds of elements combinatorial recurrences that can be used to compute exact significance levels for small sample sizes are presented for runs distributions for 2 kinds of elements critical values for small sample sizes are tabled for 2 1 6 more extensive tables are available from the author

backlund transformations and loop group actions we construct a local action of the group of rational maps from 2 to gl n on local solutions of flows of the zs akns sl n hierarchy we show that the actions of simple elements linear fractional transformations give local backlund transformations and we derive a permutability formula from different factorizations of a quadratic element we prove that the action of simple elements on the vacuum may give either global smooth solutions or solutions with singularities however the action of the subgroup of the rational maps that satisfy the u n reality condition on the space of global rapidly decaying solutions of the flows in the u n hierarchy is global and the action of a simple element gives a global backlund transformation the actions of certain elements in the rational loop group on the vacuum give rise to explicit time periodic multisolitons multibreathers we show that this theory generalizes the classical backlund theory of the sine gordon equation the group structures of backlund transformations for various hierarchies are determined by their reality conditions we identify the reality conditions the group structures for the sl n u k n k kdv kupershmidt wilson and gel fand dikii hierarchies the actions of linear fractional transformations that satisfy a reality condition modulo the center of the group of rational maps give backlund and darboux transformations for the hierarchy defined by the reality condition since the factorization cannot always be carried out under this reality condition the action is again local and backlund transformations only generate local solutions for these hierarchies unless singular solutions are allowed 2000 john wiley sons inc

an improved bonferroni inequality and applications summary we present an improved bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events the bound is constructed in terms of the joint probability of pairs of events which are represented by edges on a graph examples of applications to periodicity location shift detection kolmogorovsmirnov tests and outlier detection are given

approximating the distribution of the scan statistic using moments of the number of clumps abstract let x 1 x 2 xn be randomly distributed points on the unit interval let nx x d be the number of these points contained in the interval x x d the scan statistic nd is defined as the maximum number of points in a window of length d that is nd sup x nx x d this statistic is used to test for the presence of nonrandom clustering we say that m points form an m d clump if these points are all contained in some interval of length d let y denote the number of m d clumps in this article we show how to compute the lower order moments of y and we use these moments to obtain approximations and bounds for the distribution of the scan statistic nd our approximations are based on using the methods of moments technique to approximate the distribution of y we try two basic types of methods of moments approximations one involving a simple markov chain model and others using various different compound poisson approximations our results compare favorably with other approximations and bounds

on the distributions of scan statistics abstract this article considers the distribution of the scan statistic over some interval of the real line both for a fixed number of independent uniform points and for a poisson process it provides a new series method of calculating this distribution in the poisson case and a simple self contained recursive approximation in the fixed case these results work best at low densities which is precisely the case when the closed formulas are computationally impractical the results are compared with values tabulated by neff and naus 1980 and with a recent approximation due to naus 1982 there is also an explanation of why naus s approximation is good in the poisson case and a derivation of recursive bounds in the fixed case

detecting sparse signals in random fields with an application to brain mapping brain mapping data have been modeled as gaussian random fields and local increases in mean are detected by local maxima of a random field of test statistics derived from these data accurate p values for local maxima are readily available for isotropic data based on the expected euler characteristic of the excursion set of the test statistic random field in this article we give a simple method for dealing with nonisotropic data our approach has connections to the model of sampson and guttorp for nonisotropy in which there exists an unknown mapping of the support of the data to a space in which the random fields are isotropic heuristic justification for our approach comes from the nash embedding theorem formally we show that our method gives consistent unbiased estimators for the true p values based on new results of taylor and adler for random fields on manifolds which replace the euclidean metric by the variogram the results are used to detect gender differences in the cortical thickness of the b

approximations for the tail probabilities and moments of the scan statistic the scan statistic is used to test the hypothesis that the observed events occur at random uniformly distributed in time or space versus the hypothesis that they cluster within a moving window of size w to implement the testing procedure based on the scan statistic its tail probabilities have to be effectively evaluated in this article a survey of results on the approximations of the distribution of the scan statistic and its moments is presented numerical results comparing these approximations are also given numerous references with applications in epidemiological studies using the scan statistics are mentioned related scan statistics that have been used in many other interesting applications are listed in the reference section the article concludes with the presentation of unsolved problems related to the scan statistic

on stability for symmetric hyperbolic systems ii in a very wide spectrum of applications the problem of stability plays a central role there is a vast literature available in the field but still the problem is solved only in special cases the incompleteness of the literature is especially noticeable when the governing equations are partial differential equations the normal procedure in a stability research for such equations is to linearize the equations of perturbation and confine the study to the simpler linear equations without any mathematical justification even though the linearization has been mathematically justified only in a few very special cases it is a fact that usually the linear stability criteria are in excellent agreement with experimental observations in this paper we shall also confine our study to linear partial differential equations the conventional approach to the problem of stability for such equations is the so called normal mode method which under certain restrictions transfers the problem to an eigenvalue problem for a partial differential operator with boundary conditions in general this eigenvalue problem is very complicated it is therefore customary to restrict the study to the special cases where the problem essentially is transferred to an eigenvalue problem for an ordinary differential operator even in these special cases the eigenvalue problem is not completely resolved an alternative approach which has been given some attention in recent years is liapunov s direct method which in principle can be applied to all kinds of stability problems including nonlinear problems the results obtained by this method so far however are rather limited the difficulties in applying the method consist of constructing functionals with specific properties a new approach to the problem of stability for linear hyperbolic equations was given by eckhoff i on a somewhat speculative and conjectural basis the approach is based on the generalized progressing wave expansion method described by friedlander 2 and ludwig 3 and it has been applied to problems of stability in fluid mechanics by eckhoff and storesletten 4 51 the purpose of this paper is to give a rigorous

distribution of runs and longest runs a new generating function approach exact distributions of run statistics are traditionally obtained using combinatorial methods which under certain situations become very tedious run distributions of multiple object systems although appearing frequently in applications from various fields such as computational biology are not commonly used due in part to the lack of easy to use formulas in this article a method for evaluating partition functions of lattice models in the field of statistical mechanics is used to develop a systematic method to study various run statistics in multiple object systems by using particular generating functions for the specified situation under study many new distributions can be obtained in a unified and coherent way the method makes it possible to manipulate formulas of run statistics by using binomial identities to obtain more general yet simpler formulas to illustrate the applications of the general method the distributions of the total number of runs and the longest runs are investigated nove

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

extension of the module of invertible transformations classification of integrable systems we demonstrate that for the systems of equations which are invariant under a point group or possess conservation laws of the zeroth or first order a nontrivial extension of the module of invertible transformations is possible that simplifies greatly a classification of the integrable systems of equations here we present an exhaustive list and a classification of the second order systems of the formu t u xx f u v u x v x v t v xx g u v u x v x which possess the conservation laws of higher order the reduction group approach allows us to define the lax type representations for some new equations of our list

modified sequentially rejective multiple test procedures abstract suppose that n hypotheses h 1 h 2 h n with associated test statistics t 1 t 2 t n are to be tested by a procedure with experimentwise significance level the probability of rejecting one or more true hypotheses smaller than or equal to some specified value a commonly used procedure satisfying this condition is the bonferroni b procedure which consists of rejecting h i for any i iff the associated test statistic t i is significant at the level n holm 1979 introduced a modified bonferroni procedure with greater power than the b procedure under holm s sequentially rejective bonferroni srb procedure if any hypothesis is rejected at the level n the denominator of for the next test is n 1 and the criterion continues to be modified in a stagewise manner with the denominator of reduced by 1 each time a hypothesis is rejected so that tests can be conducted at successively higher significance levels holm proved that the experimentwise significance level

likelihood ratio tests for a change in the multivariate normal mean abstract a sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors and we wish to test that the mean vectors have changed after an unknown point in the sequence the likelihood ratio test is based on the maximum hotelling t 2 for the sequences before and after the change point the main result is a conservative approximation for its null distribution based on an improved bonferroni inequality if the change is judged significant then further changes are estimated by splitting the two subsequences formed by the first change point the methods can also be used to test for a change in row probabilities of a contingency table allowing for extramultinomial variation the results are used to find changes in a set of geological data previously analyzed by chernoff 1973 by the faces method and to find changes in the frequencies of pronouns in the plays of shakespeare

a useful upper bound for the tail probabilities of the scan statistic when the sample size is large abstract although a number of approximations to the distribution under uniformity of the scan statistic are known they are when the sample size is large either difficult to compute or numerically unstable a simple upper bound for the upper tail of the distribution based on a result of hunter 1976 is derived it is found that for large sample sizes and a reasonably wide range of window widths this bound gives a numerically stable approximation that is sufficiently accurate for hypothesis testing purposes

testing for a pulse in seasonal event data most tests for seasonal clustering are sensitive to the peak in incidence in some season 90 day interval followed by a trough 6 months later we present two statistics sensitive to a relatively sharp increase in disease incidence for a season superimposed on a constant incidence over the entire year the ratchet scan based on the maximum number of events in k consecutive months and the continuous circular scan the maximum number of events in d consecutive days we tabulate the tail distribution of the ratchet scan for n less than or equal to 35 and k 2 and 3 and find the asymptotic distribution which is applicable for n greater than or equal to 50 when k 2 or 3 we evaluate an approximation for the distribution of the continuous scan the statistics are applied to investigate seasonal clustering of adolescent suicide in the united states an illustration is given of the application of the circular scan and a small simulation study and the example are used to compare the statistics with others proposed in the literature language en

rejecton of a single outiier in two or three way layouts accurate bounds are presented for the fractiles of the maximum normed residual which is often used to test for a single outlier for two and three way layouts it is shown that the second bonferroni bound of the critical value while not conservative is an excellent approximation to the critical value being much more accurate than the first bonferroni upper bound the third bonferroni upper bound which although conservative is expensive to calculate agrees with the second bound to at least four decimal places for all factor combinations considered in this paper

transition models for change point estimation in logistic regression although a wide variety of change point models are available for continuous outcomes few models are available for dichotomous outcomes this paper introduces transition methods for logistic regression models in which the dose response relationship follows two different straight lines which may intersect or may present a jump at an unknown change point in these models the logit includes a differentiable transition function that provides parametric control of the sharpness of the transition at the change point allowing for abrupt changes or more gradual transitions between the two different linear trends as well as for estimation of the location of the change point linear linear logistic models are particular cases of the proposed transition models we present a modified iteratively reweighted least squares algorithm to estimate model parameters and we provide inference procedures including a test for the existence of the change point these transition models are explored in a simulation study and they are used to evaluate the existence of a change point in the association between plasma glucose after an oral glucose tolerance test and mortality using data from the mortality follow up of the second national health and nutrition examination survey

distribution theory of runs a markov chain approach abstract the statistics of the number of success runs in a sequence of bernoulli trials have been used in many statistical areas for almost a century even in the simplest case of independent and identically distributed bernoulli trials the exact distributions of many run statistics still remain unknown departing from the traditional combinatorial approach in this article we present a simple unified approach for the distribution theory of runs based on a finite markov chain imbedding technique our results cover not only the identical bernoulli trials but also the nonidentical bernoulli trials as a byproduct our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run

matching rectangles in d dimensions algorithms and laws of large numbers abstract for each point of the integer lattice zd let x and y be independent identically distributed random variables with p x y p 0 1 let s n be the volume of the largest d dimensional cube in 1 n d with the property that x y at every point of the cube r n is similarly defined to be the maximum volume of perfectly matching rectangles it is proved that if all possible shifts of the x lattice relative to the y lattice are allowed p lim n s n log n lim n r n log n 2d 1 where log is to base 1 p the corresponding limit without shifts is d algorithms to find largest squares and rectangles with and without shifts are also given

reductions of n wave interactions related to low rank simple lie algebras i z2 reductions the analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem we show how the second order reductions of the n wave interactions related to low rank simple lie algebras g can be embedded also in the weyl group of g this allows us to display along with the well known ones a number of new types of integrable n wave systems some of the reduced systems find applications to nonlinear optics

twisted hierarchies associated with the generalized sine gordon equation twisted u and twisted u k hierarchies are soliton hierarchies introduced by terng to find higher flows of the generalized sine gordon equation twisted o j j o j o j hierarchies are among the most important classes of twisted hierarchies in this paper we derive explicit interesting first and higher flows of twisted o j j o j o j hierarchies justify that the one dimensional systems of twisted o j j o j o j hierarchies for j iq n q 1 q n 1 called the generalized sinh gordon equations are the gauss codazzi equations for n dimensional timelike submanifolds with constant sectional curvature 1 and index q in pseudo euclidean 2n 1 dimensional space r2q 12n 1 with index 2q 1 furthermore a unified treatment of the inverse scattering theory for twisted o j j o j o j hierarchies is provided

variable coefficient wave equations with exact spreading solutions we discuss a family of variable coefficient linear wave equations that are exactly solved by a generalization of progressing waves that spread out as they propagate this can be viewed as a generalization to some variable coefficient equations of the dispersion theory method that is standard for constant coefficient equations the method is illustrated by solving some physically interesting equations

on the classification of automorphic lie algebras the problem of reduction of integrable equations can be formulated in a uniform way using the theory of invariants this provides a powerful tool of analysis and it opens the road to new applications of automorphic lie algebras beyond the con text of integrable systems in this paper it is shown that sl2 c based automorphic lie algebras associated to the icosahedral group i the octahedral group o the tetrahedral group t and the dihedral group dn are isomorphic the proof is based on techniques from classical invariant theory and makes use of clebsch gordan decomposition and transvectants molienfunctionsandthetrace form thisresultprovidesacompleteclas sification of sl2 c based automorphic lie algebras associated to finite groups when the group representations are chosen to be the same and it is a crucial step towards the complete classification of automorphic lie algebras

unbiased split variable selection for random survival forests using maximally selected rank statistics the most popular approach for analyzing survival data is the cox regression model the cox model may however be misspecified and its proportionality assumption may not always be fulfilled an alternative approach for survival prediction is random forests for survival outcomes the standard split criterion for random survival forests is the log rank test statistic which favors splitting variables with many possible split points conditional inference forests avoid this split variable selection bias however linear rank statistics are utilized by default in conditional inference forests to select the optimal splitting variable which cannot detect non linear effects in the independent variables an alternative is to use maximally selected rank statistics for the split point selection as in conditional inference forests splitting variables are compared on the p value scale however instead of the conditional monte carlo approach used in conditional inference forests p value approximations are employed we describe several p value approximations and the implementation of the proposed random forest approach a simulation study demonstrates that unbiased split variable selection is possible however there is a trade off between unbiased split variable selection and runtime in benchmark studies of prediction performance on simulated and real datasets the new method performs better than random survival forests if informative dichotomous variables are combined with uninformative variables with more categories and better than conditional inference forests if non linear covariate effects are included in a runtime comparison the method proves to be computationally faster than both alternatives if a simple p value approximation is used copyright 2017 john wiley sons ltd

reductions of integrable equations on a iii type symmetric spaces we study a class of integrable nonlinear differential equations related to the a iii type symmetric spaces these spaces are realized as factor groups of the form su n s u n k u k we use the cartan involution corresponding to this symmetric space as an element of the reduction group and restrict generic lax operators to this symmetric space the symmetries of the lax operator are inherited by the fundamental analytic solutions and give a characterization of the corresponding riemann hilbert data

an approximation for the distribution of the scan statistic the scan statistic evaluates whether an apparent cluster of disease in time is due to chance the statistic employs a moving window of length w and finds the maximum number of cases revealed through the window as it scans or slides over the entire time period t computation of the probability of observing a certain size cluster under the hypothesis of a uniform distribution is infeasible when n the total number of events is large and w is of moderate or small size relative to t we give an approximation that is an asymptotic upper bound easy to compute and for the purposes of hypothesis testing more accurate than other approximations presented in the literature the approximation applies both when n is fixed and when n has a poisson distribution we illustrate the procedure on a data set of trisomic spontaneous abortions observed in a two year period in new york city

reliability computing method for generalized k out of n system the generalized k out of n f system g k n f consists of n modules ordered in a line or circle the ith module is composed of ni components in parallel ni1 i 1 2 n the g k n f fails if and only if there exist at least f failed components or if there exist at least k consecutive failed modules to evaluate the reliability of g k n f we introduce the concept of a generalized sequence of multivariate bernoulli trials gmvbt and define the bivariate run statistic based on this sequence we bring out the relation between the probability distribution of the bivariate run statistic and the reliability of g k n f we demonstrate the evaluation of reliability of g k n f and some other related systems through a numerical example

approximations for distributions of scan statistics abstract certain statistical applications deal with the extremal distributions of the number of points in a moving interval or window of fixed length this article gives an approximation that is highly accurate for several of these distributions applications include the maximum cluster of points on a line or circle multiple coverage by subintervals or subarcs of fixed size the length of the longest success run in bernoulli trials and the generalized birthday problem

multinomial runs tests to detect clustering in constrained free recall abstract psychologists often want to detect category structure in subjects free recall protocols although runs tests based on the binomial distribution are commonly used to detect nonrandomness within a sequence many research situations require tests based on the multinomial distribution we propose a test of randomness versus clustering based on the number of runs in multinomial data we illustrate its use with data from a mass communication experiment using a constrained free recall procedure

a twisted integrable hierarchy with d2 symmetry a loop algebra approach to the gerdjikov mikhailov valchev gmv equation is provided to exploit the associated twisted integrable structure and a new twisted integrable hierarchy is discovered using the twisted loop algebra structure we obtain a transparent treatment of the associated scattering and inverse scattering theory and solve the initial value problem for the gmv equation

testing for a two phase multiple regression maximum likelihood methods are used to estimate the parameters of two separate multiple regressions that switch at an unknown point in the data normal errors with constant variance are assumed and likelihood ratio statistics are used to test for the presence of two separate regressions our main result is a conservative bound on the null distribution function of the test statistic this bound is based on an improved bonferroni inequality and a simple power series approximation is provided similar bounds are given for likelihood ratio statistics that test for a shift in the constant term of the regression only the accuracies of the bounds and approximations are evaluated on a number of examples

a multivariate change point model for statistical process control multivariate statistical process control spc carries out ongoing checks to ensure that a process is in control these checks on the process are traditionally done by t2 multivariate cusum and multivariate exponentially weighted moving average control charts these traditional spc charts assume that the in control true parameters are known exactly and use these assumed true values to set the control limits the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample it is increasingly recognized that this phase i study needs to involve large samples if the parameter estimates are to provide run behavior matching that of the known parameter situation but apart from the general undesirability of large and thus expensive studies preliminary to actual charting some industrial settings have a paucity of relevant data for estimating the process parameters an attractive alternative to traditional charting methods when mon

run probabilities in sequences of markov dependent trials abstract the probability of the occurrence of a run r is obtained as a function of the composition of r the number n of trials and the probabilities of the v 2 possible outcomes at each trial the run r can consist of any specified sequence of outcomes and the probability that one or more of a given collection of runs occurs is also evaluated the probabilities of the v possible outcomes can vary arbitrarily from trial to trial and can be l order markov dependent on the l preceding outcomes the practical application of these results is discussed

on runs and longest run tests a method of finite markov chain imbedding abstract in this article under very general assumptions on bernoulli trials a simple numerical method based on the finite markov chain imbedding technique is systematically developed to determine a the joint distribution of the number of success runs and the number of successes b the conditional distribution of the number of success runs given the number of successes that is the exact distribution of the success runs test statistic c the joint distribution of the length of the longest success run and the number of successes and d the conditional distribution of the length of the longest success run given the number of successes that is the exact distribution of the longest success run test statistic the critical regions and powers of these two tests success runs and longest success run are derived under the null hypothesis of independence and identical distribution iid as well as under the alternative hypothesis of markov dependence the application of the success runs test is illust

a path length inequality for the multivariate t distribution with applications to multiple comparisons abstract this article presents a new inequality for the multivariate t distribution which implies a new method for multiple comparisons whose foundation rests on a recent inequality due to naiman the new method is promising in view of the fact that it utilizes information estimator intercorrelations ignored by the most widely used multiple comparison methods yet is not computationally prohibitive requiring only the numerical evaluation of a single one dimensional integral in this article the validity of the new method in the normal theoretic general linear model is established and efficiency studies relative to the methods of scheffe bonferroni sidak and hunter worsley are presented the new method is shown to always improve on scheffe s method the new method is also shown to perform well that is to lead to a smaller critical point than its competitors with low degrees of freedom but the method is not as efficient as the hunter worsley method for high degrees of freedom in addition the me

reduction groups and automorphic lie algebras we study a new class of infinite dimensional lie algebras which has important applications to the theory of integrable equations the construction of these algebras is very similar to the one for automorphic functions and this motivates the name automorphic lie algebras for automorphic lie algebras we present bases in which they are quasigraded and all structure constants can be written out explicitly these algebras have useful factorisations on two subalgebras similar to the factorisation of the current algebra on the positive and negative parts

probability bounds with cherry trees a third order upper bound is presented on the probability of the union of a finite number of events by means of graphs called cherry trees these are graphs that we construct recursively in such a way that every time we pick a new vertex connect it with two already existing vertices if the latters are always adjacent we call the cherry tree a t cherry tree a cherry tree has a weight that provides us with the upper bound on the union any hunter worsley bound can be majorized by a t cherry bound constructed by the use of the hunter worsley tree a cherry tree bound can be identified as a feasible solution to the dual of the boolean probability bounding problem a t cherry tree bound can be identified as the objective function value of the dual vector corresponding to a dual feasible basis in the boolean problem this enables us to improve on the bound algorithmically if we use the dual method of linear programming

generalized maximally selected statistics maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures this powerful framework contains most of the published procedures in this area as special cases such as maximally selected chi squared and rank statistics but also allows for direct construction of new test procedures for less standard test problems as an application a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions this new test is employed to search for a high risk group of rectal cancer patients treated with a neo adjuvant chemoradiotherapy moreover a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints

correction of the p value after multiple coding of an explanatory variable in logistic regression we propose a method and a program to determine a significance level for a series of codings of an explanatory variable in logistic regression dichotomous and box cox transformations are considered three methods of correcting the significance level are studied the bonferroni method efron s method which uses the correlation between successive tests and the exact calculation by numerical integration using all correlations a simulation study has led to a strategy for the choice and number of the different codings of the variable this method is illustrated using the data of a study of the relation between cholesterol and dementia

statistical method for detecting structural change in the growth process due to competition among individual trees and other exogenous factors that change the growth environment each tree grows following its own growth trend with some structural changes in growth over time in the present article a new method is proposed to detect a structural change in the growth process we formulate the method as a simple statistical test for signal detection without constructing any specific model for the structural change to evaluate the p value of the test the tube method is developed because the regular distribution theory is insufficient using two sets of tree diameter growth data sampled from planted forest stands of cryptomeria japonica in japan we conduct an analysis of identifying the effect of thinning on the growth process as a structural change our results demonstrate that the proposed method is useful to identify the structural change caused by thinning we also provide the properties of the method in terms of the size and power of the test

power of the scan statistic for detection of clustering the scan statistic is the maximum number of events in an interval of fixed length w as the subinterval moves over the entire time frame previous research derived the null distribution of the scan statistic under the conditional model which assumed that the total number of events was fixed and under the unconditional model which let the total number of events be a random variable this paper derives approximations for the power of the scan test for a pulse alternative under this alternative the relative risk of disease on a subinterval tau tau w tau unknown is theta fold as high as it is for other subintervals of length w two sets of approximations are given for each model the first approximation gives highly accurate results but requires use of a personal computer the second procedure can be performed on a hand held calculator and appears very accurate for the cases examined

on dispersion for linear waves in nonuniform media motivated by several well known examples of linear waves in uniform media a general definition of a dispersionfree wave valid for both uniform and nonuniform media is set up examples of dispersionfree generalizations of the classical wave equation to nonuniform media are given although dispersionfree waves are exceptional both in the uniform and in the nonuniform case it is proved that hyperbolic systems have the property that in the limit of short wavelengths the solutions behave like a linear combination of dispersionfree waves on that basis it is possible to study the dispersion properties of hyperbolic waves by an asymptotic expansion explicit calculations are given for such expansions for a family of generalizations of the classical wave equation to nonuniform media

approximations and bounds for the distribution of the scan statistic abstract the scan statistic is used in many areas of science to test the null hypothesis of uniformity against a clustering alternative this article derives approximations and bounds for the distribution of scan statistics an extensive simulation study is carried out to compare the approximations and the bounds derived in this article with other known approximations and bounds the new lower and upper bounds that have been derived are very useful in evaluating the approximations and the simulation a quantity of average number of points in the scanning interval of length d d is introduced to study the approximations for the distribution of the scan statistic for low values of d the approximation derived in this article is the most accurate one the importance of the scan statistics arises from their applications in many areas including nuclear physics geology radio optics photography and epidemiology

reductions of integrable equations dihedral group we discuss the algebraic and analytic structure of rational lax operators with algebraic reductions of lax equations we associate a reduction group a group of automorphisms of the corresponding infinite dimensional lie algebra we present a complete study of dihedral reductions for sl 2 c lax operators with simple poles and corresponding integrable equations in the last section we give three examples of dihedral reductions for sl n c lax operators