The generalized lognormal distribution and the Stieltjes moment problem

This paper studies a Stieltjes-type moment problem defined by the generalized lognormal distribution, a heavy-tailed distribution with applications in economics, finance and related fields. It arises as the distribution of the exponential of a random variable following a generalized error distribution, and hence figures prominently in the EGARCH model of asset price volatility. Compared to the classical lognormal distribution it has an additional shape parameter. It emerges that moment (in)determinacy depends on the value of this parameter: for some values, the distribution does not have finite moments of all orders, hence the moment problem is not of interest in these cases. For other values, the distribution has moments of all orders, yet it is moment-indeterminate. Finally, a limiting case is supported on a bounded interval, and hence determined by its moments. For those generalized lognormal distributions that are moment-indeterminate Stieltjes classes of moment-equivalent distributions are presented.Comment: 12 pages, 1 figur

When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries where the underlying data is available only over limited interfaces which provide lookup access to the tuples matching a given binding, but possibly restricting the number of output tuples returned. Interfaces imposing such "result bounds" are common in accessing data via the web. Given a query over a set of relations as well as some integrity constraints that relate the queried relations to the data sources, we examine the problem of deciding if the query is answerable over the interfaces; that is, whether there exists a plan that returns all answers to the query, assuming the source data satisfies the integrity constraints. The first component of our analysis of answerability is a reduction to a query containment problem with constraints. The second component is a set of "schema simplification" theorems capturing limitations on how interfaces with result bounds can be useful to obtain complete answers to queries. These results also help to show decidability for the containment problem that captures answerability, for many classes of constraints. The final component in our analysis of answerability is a "linearization" method, showing that query containment with certain guarded dependencies -- including those that emerge from answerability problems -- can be reduced to query containment for a well-behaved class of linear dependencies. Putting these components together, we get a detailed picture of how to check answerability over result-bounded services.Comment: 45 pages, 2 tables, 43 references. Complete version with proofs of the PODS'18 paper. The main text of this paper is almost identical to the PODS'18 except that we have fixed some small mistakes. Relative to the earlier arXiv version, many errors were corrected, and some terminology has change

Towards an Abstract Domain for Resource Analysis of Logic Programs Using Sized Types

We present a novel general resource analysis for logic programs based on sized types.Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of terms and their subterms at any position and depth. They also allow relating the sizes of terms and subterms occurring at different argument positions in logic predicates. Using these sized types, the resource analysis can infer both lower and upper bounds on the resources used by all the procedures in a program as functions on input term (and subterm) sizes, overcoming limitations of existing analyses and enhancing their precision. Our new resource analysis has been developed within the abstract interpretation framework, as an extension of the sized types abstract domain, and has been integrated into the Ciao preprocessor, CiaoPP. The abstract domain operations are integrated with the setting up and solving of recurrence equations for both, inferring size and resource usage functions. We show that the analysis is an improvement over the previous resource analysis present in CiaoPP and compares well in power to state of the art systems.Comment: Part of WLPE 2013 proceedings (arXiv:1308.2055

When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries on data available through access methods, that provide lookup access to the tuples matching a given binding. Such interfaces are common on the Web; further, they often have bounds on how many results they can return, e.g., because of pagination or rate limits. We thus study result-bounded methods, which may return only a limited number of tuples. We study how to decide if a query is answerable using result-bounded methods, i.e., how to compute a plan that returns all answers to the query using the methods, assuming that the underlying data satisfies some integrity constraints. We first show how to reduce answerability to a query containment problem with constraints. Second, we show "schema simplification" theorems describing when and how result bounded services can be used. Finally, we use these theorems to give decidability and complexity results about answerability for common constraint classes.Comment: 65 pages; journal version of the PODS'18 paper arXiv:1706.0793

The idea of words as signs

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The Design of Arbitrage-Free Data Pricing Schemes

Motivated by a growing market that involves buying and selling data over the web, we study pricing schemes that assign value to queries issued over a database. Previous work studied pricing mechanisms that compute the price of a query by extending a data seller's explicit prices on certain queries, or investigated the properties that a pricing function should exhibit without detailing a generic construction. In this work, we present a formal framework for pricing queries over data that allows the construction of general families of pricing functions, with the main goal of avoiding arbitrage. We consider two types of pricing schemes: instance-independent schemes, where the price depends only on the structure of the query, and answer-dependent schemes, where the price also depends on the query output. Our main result is a complete characterization of the structure of pricing functions in both settings, by relating it to properties of a function over a lattice. We use our characterization, together with information-theoretic methods, to construct a variety of arbitrage-free pricing functions. Finally, we discuss various tradeoffs in the design space and present techniques for efficient computation of the proposed pricing functions.Comment: full pape