A New Distribution Family for Microarray Data †

In this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such as moments, asymmetry and kurtosis coefficients, are derived. Particular cases of interest based on the normal, logistic, Laplace and Cauchy models are discussed in depth. The estimation of parameters is carried out by applying moments and maximum likelihood methods. Also, a simulation study was conducted to illustrate the good performance of estimators. An application to the Survival Times (in days) of Guinea Pigs dataset is included, where the special cases of distributions in this family are fitted. The option which provides the best fit is ultimately chosen. An R package, called “tpn”, has been implemented, which includes the relevant cases of interest in this family.

Recently, many researchers have been searching for a new family of distributions that improves the fit to a specific dataset and has attractive properties. In this paper, we present a flexible method for constructing continuous distributions by controlling their reliability. Our new technique incorporates a single parameter into the chosen continuous distribution, but it is a novel method and independent of any previously used methods. We present two special cases of this family. The new modified family offers significant improvements in fit and applicability in many fields. Furthermore, the maximum likelihood method is used to estimate the parameters in the proposed family. Real data analysis is performed to demonstrate the suitability of the new family.

We proposed a new family of distributions called the Topp Leone exponentiated-G family of distributions with two extra positive shape parameters, which generalizes and also extends the Topp Leone-G family of distributions. We derived some mathematical properties of the proposed family including explicit expressions for the quantile function, ordinary and incomplete moments, generating function and reliability. Some sub-models in the new family were discussed. The method of maximum likelihood was used to estimate the parameters of the sub-model. Further, the potentiality of the family was illustrated by fitting two real data sets to the mentioned sub-models.

We introduce a new family of distributions using intervened power series distribution. It is a rich family containing distributions such as Marshall–Olkin extended families of distributions, families of distributions generated through truncated negative binomial, and families of distributions generated through truncated binomial distribution. Also, the proposed distribution is a generalization of the families of distributions generated through zero truncated Poisson distribution. As a particular case, we study exponential intervened Poisson (EIP) distribution. This is a generalization of exponential-Poisson distribution. The shape properties of the pdf and hazard rate are proved. The model identifiability is established. The expression for moments, mean deviation, distribution of order statistics, and residual life function of EIP distribution are derived. The unknown parameters of the distribution are estimated using the method of maximum likelihood. The existence and uniqueness of maximum likelihood estimates (MLEs) are proved. Simulation study is carried out to show the performance of MLEs. EIP distribution is fitted to two real data sets and it is shown that the distribution is more appropriate than other competitive models. The adequacy of the EIP model for the data set is established using parametric bootstrap approach.

The combined maximum entropy and likelihood method has been applied to the determination of a previously unknown organic crystal structure, toluene-p-sulfonhydrazide (p-CH3C6H4SO2NHNH2), directly from X-ray powder diffraction data. The partial structure solution obtained using the maximum entropy technique was closer to the final refined structure than was the partial structure solution generated by conventional direct methods calculations. The structure is monoclinic, P21/n, a= 18.6021(6)A, b= 5.6406(2)A, c= 8.5356(3)A, β= 106.22(2)°.

DNA microarray data is a challenging issue for machine learning researchers due to the high number of gene expression contained and the small samples sizes. To deal with this problem, feature selection methods, such as filters and wrappers, are typically applied to reduce the dimensionality. In this work, we apply a filter method before the classification and include a discretization step. The results obtained over ten different microarray data sets confirm the adequacy of the proposed method, that achieves better performances than the classifier alone. Besides, the combination method is also compared with the approaches of other authors (using wrappers and filters), outperforming the prediction accuracy and maintaining or even decreasing the number of genes required.

ABSTRACTThis paper presents a new family of distributions for count data, the so called zero-modified power series (ZMPS), which is an extension of the power series (PS) distribution family, whose support starts at zero. This extension consists in modifying the probability of observing zero of each PS distribution, enabling the new zero-modified distribution to appropriately accommodate data which have any amount of zero observations (for instance, zero-inflated or zero-deflated data). The Hurdle distribution version of the ZMPS distribution is presented. PS distributions included in the proposed ZMPS family are the Poisson, Generalized Poisson, Geometric, Binomial, Negative Binomial and Generalized Negative Binomial distributions. The paper also describes the properties and particularities of the new distribution family for count data. The distribution parameters are estimated via maximum likelihood method and the use of the new family is illustrated in three real data sets. We emphasize that the new distribution family can accommodate sets of count data without any previous knowledge on the characteristic of zero-inflation or zero-deflation present in the data.

Marshall and Olkin (Biometrika 641–652, 1997) introduced a new way of incorporating a parameter to expand a family of distributions. In this paper we adopt the Marshall-Olkin approach to introduce an extra shape parameter to the two-parameter generalized exponential distribution. It is observed that the new three-parameter distribution is very flexible. The probability density functions can be either a decreasing or an unimodal function. The hazard function of the proposed model, can have all the four major shapes, namely increasing, decreasing, bathtub or inverted bathtub types. Different properties of the proposed distribution have been established. The new family of distributions is analytically quite tractable, and it can be used quite effectively, to analyze censored data also. Maximum likelihood method is used to compute the estimators of the unknown parameters. Two data sets have been analyzed, and the results are quite satisfactory.

In this paper, we introduce two new families of distributions containing unimodal as well as bimodal and trimodal distributions. The models extend the normal model to trimodal symmetric and asymmetric situations, and typically involve fewer parameters to be estimated than the mixtures of normal distributions. Statistical properties of these new families are studied in detail. The problem of estimating parameters is addressed by considering the maximum likelihood method and Fisher information matrices are derived. A small Monte Carlo simulation study is conducted to examine the performance of the obtained estimators. The methodology developed is illustrated with three real data applications.

The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, occur when the recorded data have the probability proportional to an increasing function of absolute value of deviations. In this paper a new family of distributions called double normal family of distribution is introduced and characterized. This symmetric family is a subclass of the univariate Kotz type distributions. The normal distribution is a special case of this family. Estimation of location and scale parameters by moment and maximum likelihood methods are given. Some pivotal quantity are introduced. Confidence intervals for some parameters by numerical methods are given.

A two-stage approach to semilinear in-slide models

In biometric systems, people may be asked to provide multiple scans for redundancy and quality control. In the case of fingerprint matching systems, repeat fingerprint probes of the same physical finger can be available and data from such multiple samples can be fused for reliable authentication of individuals. Since multiple samples are from the same instance of the finger, some relationships between them, e.g. diversity or similarity, could be observed. In this paper, we investigate such relationships and use them in fusion in order to improve the performance of biometric systems. The relationships between samples are derived by measuring the similarity between matching score vectors with Pearson's correlation and cosine similarity measures. We conduct experiments using the FVC2002 dataset consisting of four fingerprint databases and trainable combination methods, likelihood ratio and multilayer perceptron. The results show that utilization of similarity measures for matching scores can further improve the multi-sample biometric fusion in both combination methods.

Felsenstein, J. (Department of Genetics SK-50, University of Washington, Seattle, Washington 98195). 1973. Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters. Syst. Zool. 22:240-249.The general maximum likelihood approach to the statistical estimation of phylogenies is outlined, for data in which there are a number of discrete states for each character. The details of the maximum likelihood method will depend on the details of the probabilistic model of evolution assumed. There are a very large number of possible models of evolution. For a few of the simpler models, the calculation of the likelihood of an evolutionary tree is outlined. For these models, the maximum likelihood tree will be the same as the parsimonious (or minimum-steps) tree if the probability of change during the evolution of the group is assumed a priori to be very small. However, most sets of data require too many assumed state changes per character to be compatible with this assumption. Farris (1973) has argued that maximum likelihood and parsimony methods are identical under a much less restrictive set of assumptions. It is argued that the present methods are preferable to his, and a counterexample to his argument is presented. An algorithm which enables rapid calculation of the likelihood of a phylogeny is described. [Evolutionary trees: maximum likelihood.] The first systematic attempt to apply standard statistical inference procedures to the estimation of evolutionary trees was the work of Edwards and Cavalli-Sforza (1964; see also Cavalli-Sforza and Edwards, 1967). At about the same time, the parsimony' or minimum evolutionary steps method of Camin and Sokal (1965) gave a great impetus to the development of welldefined procedures for obtaining evolutionary trees. Edwards and Cavalli-Sforza concerned themselves with data from continuous variables such as gene frequencies and quantitative characters. The CaminSokal approach, on the other hand, was developed for characters which are recorded as a series of discrete states. Although some taxonomists have declared that the problem of guessing phylogenies should be viewed as a problem of statistical inference (Farris, 1967, 1968; Throckmorton, 1968), until recently there have been no attempts to explore the relationship between the statistical inference and minimum-steps approaches. Recently, Farris (1973) has presented a detailed argument that, under certain reasonable assumptions, the maximum-likelihood method of statistical inference appropriate to discrete-character data is precisely the parsimony method of Camin and Sokal. In this paper, I will examine the application of maximum likelihood methods to discrete characters, and will show that parsimony methods are not maximum likelihood methods under the assumptions made by Farris. They are maximum likelihood methods under considerably more restrictive assumptions about evolution. METHODS OF MAXIMUM LIKELIHOOD Suppose that we want to estimate the evolutionary tree, T, which is to be specified by the topological form of the tree and the times of branching. We are given a set of data, D, and a model of evolution, M, which incorporates not only the evolutionary processes, but also the processes of sampling by which we obtained the data. This model will usually be probabilistic, involving random events such as changes of the environment, occurrence of favorable

The diagnosis and treatment of soft tissue sarcomas (STS) have been difficult. Of the diverse histological subtypes, undifferentiated pleomorphic sarcoma (UPS) is particularly difficult to diagnose accurately, and its classification per se is still controversial. Recent advances in genomic technologies provide an excellent way to address such problems. However, it is often difficult, if not impossible, to identify definitive disease-associated genes using genome-wide analysis alone, primarily because of multiple testing problems. In the present study, we analyzed microarray data from 88 STS patients using a combination method that used knowledge-based filtering and a simulation based on the integration of multiple statistics to reduce multiple testing problems. We identified 25 genes, including hypoxia-related genes (e.g., MIF, SCD1, P4HA1, ENO1, and STAT1) and cell cycle- and DNA repair-related genes (e.g., TACC3, PRDX1, PRKDC, and H2AFY). These genes showed significant differential expression among histological subtypes, including UPS, and showed associations with overall survival. STAT1 showed a strong association with overall survival in UPS patients (logrank p = 1.84×10−6 and adjusted p value 2.99×10−3 after the permutation test). According to the literature, the 25 genes selected are useful not only as markers of differential diagnosis but also as prognostic/predictive markers and/or therapeutic targets for STS. Our combination method can identify genes that are potential prognostic/predictive factors and/or therapeutic targets in STS and possibly in other cancers. These disease-associated genes deserve further preclinical and clinical validation.

The genus Crocodylus comprises an evolutionarily recent radiation (12 extant species) of large, aquatic Archosaurian predators. The group is likely to have an African saltwater-tolerant common ancestor and trans-oceanic migration is required to account for the current circumtropical distribution of the group. However, the phylogeny and historical biogeography of the genus remains poorly resolved. Many species have suffered recent severe declines due to a combination of habitat destruction and overharvesting associated with the crocodilian skin-trade. All species are now protected under CITES, but several remain critically endangered in the wild, including in the Indo-Pacific, the Siamese crocodile, C. siamensis, and the Philippine crocodile, C. mindorensis. Other Indo-Pacific species are intensively managed for skins, including the New Guinea crocodile, C. novaeguineae, and the estuarine crocodile, C. porosus. A complication for conservation and management of crocodiles in the Indo-Pacific region is that the distribution of genetic variation within species is unclear, and species boundaries are uncertain on the basis of morphology. There are three areas of particular concern: (i) the southern New Guinean population of C. novaeguineae may comprise an undescribed taxon on the basis of divergence in morphology and life history traits from the allopatric northern population; (ii) recent anecdotal evidence exists for a biogeographically distinct population of C. siamensis in Borneo; and (iii) a putative new species of palustrine crocodile from Borneo, C. raninus, has recently been resurrected. Clarification of the taxonomic status of freshwater Crocodylus species in the Indo- Pacific has been identified as a conservation priority by the IUCN Crocodile Specialist Group. However, no phylogeographic data has yet been collected for any Indo-Pacific crocodilian. In this thesis I combined Bayesian and maximum likelihood phylogenetic analyses of relationships within Crocodylus (Chapter 2), with population genetic and phylogeographic analyses of several Indo-Pacific species, the estuarine crocodile, C. porosus (Chapter 3), the New Guinea crocodile, C. novaeguineae (Chapter 4), and the Siamese crocodile, C. siamensis (Chapter 5). The aims of the study were to: (i) resolve the phylogeny and biogeographic history of the genus; (ii) clarify the taxonomy of phenotypically (southern-form C. novaeguineae; C. raninus) or biogeographically (Bomean C. siamensis) distinct populations of uncertain status; and (iii) discriminate historical and contemporary determinants of population structure within species in order to delimit conservation units for management. Bayesian and maximum likelihood phylogenetic analyses of mtDNA sequences (Chapter 2) revealed a monophyletic Central American clade (C acutus, C. intermedius, C. moreletii, C rhombifer), and supported trans-Atlantic colonisation of this region by an African founder closely related to the Nile crocodile, C. niloticus. Monophyly of the six Indo-Pacific species was weakly inferred, but there was strong evidence for a monophyletic lineage in which the Australian freshwater crocodile, C. johnstoni, was basal to the sibling species C. novaeguineae and C. mindorensis. A second Indo-Pacific lineage comprising C. palustris, C. porosus and C siamensis received moderate support, but relationships within this clade were poorly resolved. The putative Bomean species, C. raninus, appears to be conspecific with northern-form C. novaeguineae, although this result requires confirmation with genetic analysis of museum type specimens. The phylogenetic analysis provided a fi-amework for phylogeographic and population genetic studies within species. Intraspecific genetic diversity was minimal relative to mean interspecific divergence, particularly for C. novaeguineae, and there was no evidence for departures from existing species boundaries. Different historical and contemporary processes were found to underlie contrasting phylogeographic patterns in the three species, with less structure evident for the estuarine species, C. porosus, than for co-distributed populations of the two primarily freshwater species C. novaeguineae and C. siamensis. A strong phylogeographic break was revealed between C. siamensis on the SE Asian mainland and a sample of conspecific captive individuals purportedly sourced from the wild in eastern Borneo. This result is consistent with the existence of a remnant population in this region and with a history of past fragmentation between Borneo and the SE Asian mainland. For C. novaeguineae, mtDNA and microsatellite analyses revealed strong, but shallow, population structure that was congruent with the north-south partitioning of morphological and life history variation in this species. This suggested that the Central Highlands have not acted as a long-term biogeographic barrier to genetic exchange, but that contemporary gene flow is very limited. This recent isolation may have facilitated the development of phenotypic differentiation in the species. Both southern-form C. novaeguineae and the putative C. siamensis population in Borneo should be considered as distinct evolutionarily significant units (ESUs) for future management.In comparison, no phylogeographic structure was identified for the estuarine crocodile, C porosus, either among populations that were co-distributed with C novaeguineae and C. siamensis, or at a broader geographic scale encompassing the Indo-Malay Archipelago and Western Pacific Ocean. This suggests that the sampled C porosus populations comprise a single ESU. Nonetheless, populations were strongly structured on the basis of allele frequency differences and at least seven regional populations qualify as management units. A highly asymmetric pattern of historical gene flow orientated from western to eastern populations, and involving several episodes of range expansion coupled with recurrent gene flow, was found to underlie the distribution of mtDNA variation in C. porosus. A pattern of isolation by distance was identified for microsatellite markers, although there was no evidence for male biased gene flow. Differences in phylogeographic pattern between species may reflect a greater capacity for long-distance marine migration by C. porosus, relative to the two primarily freshwater species.The integration of phylogenetic and phylogeographic analyses in this study has addressed one of the IUCN Crocodile Specialist Group's conservation priorities by clarifying species boundaries in the Indo-Pacific freshwater species complex. Existing species boundaries were supported, but distinct ESU's were identified in the New Guinea crocodile, C. novaeguineae, and the Siamese crocodile, C. siamensis. The purported Bomean endemic species, C. raninus, does not appear to be a valid taxon. These findings will have important implications for conservation and management of crocodiles in the Indo-Pacific region.