Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work fr...

• In the insurance area, especially based on observations of the number of claims, N(w), corresponding to an exposure w, and on observations of the total amount of claims incurred, Y (w), the risk theory arises to quantify risks and to fit models of pricing and insurance company ruin. However, the main problem is the complexity to obtain the distribution function of Y (w) and, consequently, the...

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails ...

We establish empirically using three different definitions of US cities that the upper tail obeys a Pareto law and not a lognormal distribution. We emphasize estimation of a switching point between the body of the city size distribution (which includes most cities) and its upper tail (which includes most of the population). For the 2000 Census Places data, in particular, our preferred model sug...

Stochastic modeling of investment returns is an important topic for actuaries who deal with variable annuity and segregated fund investment guarantees. The traditional lognormal stock return model is simple, but it is generally less appealing for longer-term problems. In recent years, the use of regime-switching lognormal (RSLN) processes for modeling maturity guarantees has been gaining popula...

In this paper I first define the regime-switching lognormal model. Monthly data from the Standard and Poor’s 500 and the Toronto Stock Exchange 300 indices are used to fit the model parameters, using maximum likelihood estimation. The fit of the regime-switching model to the data is compared with other common econometric models, including the generalized autoregressive conditionally heteroskeda...

تناول البحث شعر الشّاعر أبي الوليد فخر الدّين محمّد بن سعيد الشَّاطبيّ، أحد الشُّعراء الأندلسيين الذين عاشوا في عصر الموحدين خلال القرن السّابع الهجري، وقد جاء أربعة مباحث: تركّز الأول على استعراض سيرة ابن الجنَّان، أما المبحث الثاني فاقتصر الموضوعات التي طرقها أشعاره، حين الثالث خصائص شعره الفنّيَّة، وتركّز الرابع جمع ما بقي من مصادر التُّراث العربي المخطوطة والمطبوعة.

We examine the shape of primordial black hole mass distribution arising from a peak in power spectrum. In light improvements to modeling, we revisit claim that effects critical collapse produce is not described by commonly assumed lognormal, showing this conclusion remains valid, particularly for narrow peaks where insensitive properties and determines minimum width. propose some alternative mo...