Mathematical Statistics

Based on the our October paper "A Generalized Viral Infection Mathematical Model Derived from Covid-19 Simulation", at a conceptual level higher than the classic SIR/SEIR model, we have established the 6 laws of infection regarding the final infection ratio within any given population without any artificial intervention and have shown the final infection ratio in a natural, non-interfered pandemic must fall within a specified lower and upper bound as 1 − 1 R 2 0 ≤ F R ≤ 2 (1 − 1 R 0). Whereas R 0 is the intrinsic R 0 value of the disease. In this paper, we show how human intervention strategies alter the previous assumptions based on 2 factors. First, artificial intervention with cycles of restricting measures and relaxations. Based on our May paper "The Predictions on Worldwide Covid-19 Pandemic Cases Based on Historical Data", we have already demonstrated the dynamic falling R 0 (t) curve during lock down measures. With more historical data and observation, we now expand the scope to include a dynamic rising R 0 (t) curve following the relaxation of measures, completing the cycle of restriction and relaxation. Second, the introduction of vaccination at a steady rate introduced a new variable into the existing infection model, we denote it as function V (t). We demonstrate the optimal strategies of vaccination interpreted within our existing established framework.

In their smash hit MATHEMATICAL STATISTICS WITH APPLICATIONS, debut creators Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a strong establishment in factual hypothesis while passing on the pertinence and significance of the hypothesis in taking care of viable issues in reality. The creators' utilization of pragmatic applications and fantastic activities encourages you find the idea of insights and comprehend its basic job in logical research.

Point estimation is one of the core topics in mathematical statistics. In this paper we consider the most common methods of point estimation: non-Bayes, Bayes and empirical Bayes methods to estimate the shape parameter of Lomax distribution based on complete data. The maximum likelihood, moment and uniformly minimum variance unbiased estimators are obtained as non-Bayes estimators. Bayes and empirical Bayes estimators are obtained corresponding to three informative priors "gamma, chi-square and inverted Levy" based on symmetric "squared error" and asymmetric "LINEX and general entropy" loss functions. The estimates of the shape parameter were compared empirically via Monte Carlo simulation study based upon the mean squared error. Among the set of conclusions that have been reached, it is observed that, for all sample sizes and different cases, the performance of uniformly minimum variance unbiased estimator is better than other non-Bayes estimators. Fur...

A method for computing Mackey-Glass equation of the form   () (), () y t f y t y t    is examined in this paper. For a given lag  , uniformly generated and fixed beta is observed for estimating the y  (density  time-units in the past). The technique was applied to blood destruction and production in human body.

We study asymptotically optimal statistical inference concerning the unknown state of N identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam's theory of Local Asymptotic Normality.

The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the
field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is
a three-dimensional phenomenon.

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

Drinking water supply is an essential public function but is at the same time exposed to risks. Since a totally risk-free society is not attainable, risks need to be managed efficiently to achieve an acceptable level of risk. A reliable supply of safe drinking water is vital and the World Health Organization emphasises an integrated risk management approach, including the entire drinking water system from source to tap. An integrated approach is important as there are interactions between different parts of a system. Efficient risk management requires appropriate risk analyses to characterise risk and support decision-making. Risk analysis based on an integrated approach facilitates well-informed decision-making and efficient use of resources for risk reduction. However, guidance on methods for integrated risk analysis of drinking water systems is limited. To support risk management of drinking water systems, a method for integrated and probabilistic risk analysis has been developed...

Während meines Studiums der Wirtschaftsinformatik an der Hochschule Harz hatte ich in den Jahren 2002 bis 2005 das große Glück, als Tutor für verschiedene Statistik-Vorlesungen von Dr. Walter Strube tätig werden zu dürfen. Zu Beginn meiner Tutorentätigkeit konnte ich eine über die Jahre von Tutor zu Tutor weiterentwickelte Aufgabensammlung in Form einer ,,Lose-Blatt-Sammlung" von meiner direkten Vorgängerin, Frau Weinert, übernehmen. Um den Studierenden die Arbeit mit den Übungsaufgaben zu erleichtern, habe ich damals für sämtliche Aufgaben Musterlösungen und Erläuterungen verfasst und den Teilnehmern meiner Tutorien in Form von Handouts zur Verfügung gestellt. In den vergangenen sieben Jahren bin ich immer wieder von Studierenden nach dieser Sammlung von Aufgaben mit Musterlösungen gefragt worden, so dass ich mich dazu entschlossen habe, sie noch einmal zu überarbeiten, mit einigen weiteren Erläuterungen zu versehen und über den GRIN-Verlag sowie verschiedene Webseiten als kostenfreien Download zur Verfügung zu stellen. Ich hoffe, dass sie so vielleicht auch für den einen oder anderen Studierenden außerhalb unserer Hochschule von Nutzen sein kann.

This article argues that any ecological finance theory devised to fit the Sustainable Development Goals (SDGs) needs a paradigm shift in the morphology of randomness underlying financial risk modelling, by integrating the characteristics of "nature" and sustainability into the modelling carried out. It extends the common diagnosis of the 2008 financial crisis with considerations on the morphology of randomness and the reasons why neoclassical finance theory is not sustainable from this perspective. It argues that the main problem with unsustainable neoclassical finance risk modelling is its underlying morphology of randomness that creates a dangerous risk culture. It presents Leibniz's principle of continuity and Quetelet's theory of average as cornerstones of classical risk culture in finance, acting as a mental model for financial experts and practitioners. It links the notion of sustainability with the morphology of randomness and presents a possible alternative approach to financial risk modelling defined by rough randomness. If morphology of randomness in nature is properly described by fractal and multifractal methods, hence ecological finance theory has to include fractal properties into financial risk models. The conclusion proposes a new agenda for future research.

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

This study aim at optimizing the parameter θ of Discrete Weibull (DW) regression obtained by maximizing the likelihood function. Also to examine the strength of three acquisition functions used in solving auxiliary optimization problem. The choice of Discrete Weibull regression model among other models for fitting count data is due to its robustness in fitting count data. Count data of hypertensive patients visits to the doctor was obtained at Medicare Clinics Ota, Nigeria, and was used for the analysis. First, parameter θ  and β  were obtained using Metropolis Hasting Monte Carlo Markov Chain (MCMC) algorithm. Then Bayesian optimization was used to optimize the parameter the likelihood function of DW regression, given β to examine what θ would be, and making the likelihood function of DW the objective function. Upper confidence bound (UCB), Expectation of Improvement (EI), and probability of Improvement (PI) were used as acquisition functions. Results showed that fitting Bayesian D...

В рамках математического учения о гармонии и развернутом междисциплинарном аспекте излагается типология последовательностей Фибоначчи, основанная на синтезе математических и математико-лингвистических представлений, включающем теорию рекурсии, алгебраических уравнений, непрерывных дробей, пропорций и средних. Широко используется визуализация результатов типологизации в виде орнаментальных фигур: крестов, клотоид, ветвящихся структур. Описывается широкий спектр приложений результатов типологизации в гуманитарных и естественных науках. Книга снабжена разнообразными примерами из области литературного творчества, теории ценозов, спорта, электротехники, теории поиска, физики, астрономии, экономики и архитектурного пропорционирования. Для экономистов, социологов, инженеров, филологов и других специалистов, интересующихся вопросами математической гармонии объектов произвольной природы.

Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of n. Using extreme value theory, we examine the properties of the hidden tail and calculate its moments of order p.

The method is useful in showing how large a bias one can expect, for a given n, between the visible  in-sample mean and the true statistical mean (or higher moments), which is considerable for alpha close to 1.

Among other properties, we note that the "hidden" moment of order 0, that is, the exceedance probability for power law distributions, follows an exponential distribution and has for expectation 1/n regardless of the parametrization of the scale and tail index.

A probabilistic (or statistical) experiment has the following characteristics: (a) the set of all possible outcomes of the experiment can be described; (b) the outcome of the experiment cannot be predicted with certainty prior to the performance of the experiment.

Gün geçtikçe bilgi üretimi üstel olarak artmakta ve dünyamız, insan bilgisini geliştirecek bir takım anlamlı bilgiler içermesi gerektiğine inandığımız verilerle dolup taşmaktadır. Bununla birlikte, anlamlı bilgi çıkarmak, büyük miktarda verinin düz metin veya geleneksel tabular biçiminde sunulması durumunda zor olmaktadır. Böylece, verilerin  etkili  grafik gösterimleri,  insan  görsel  algılama  yeteneklerini  harekete  geçirerek  popülerlik kazanmaktadır. Veri görselleştirme, insan bilgisini güçlendirmek için soyut ve fiziksel olmayan verilerin bilgisayar tabanlı  etkileşimli  görsel  temsillerinin kullanılmasıdır. Görselleştirmede,kullanıcıların  beklenen  etkinlikleri algılamaları ve keşfetmelerinin yanı sıra,veriler hakkında fikir sahibi olup beklenmedik yapıları görmelerine yardımcı olmak amaçlanır. Çok değişkenli veri görselleştirmesi için, görsel olarak analiz edilecek veri seti büyük boyutlardadır.  Belirli  bir  bilgi  görselleştirme  türü  olan  çok  değişkenli  veri  görselleştirme,  pazarlama  ve mühendislik tasarımından, endüstri ve finansal piyasalara kadar çeşitli alanlarda sayısız uygulamayı içermektedir. Bu nedenle görselleştirme birçok özellik arasındaki ilişkinin hayati öneme sahip olduğu aktif bir araştırma alanıdır. Bu  çalışmada,öncelikle  büyük  veri  konusu  hakkında  genel  bilgiler  verilmiştir.  Daha  sonra,  yaygın  olarak kullanılan  görselleştirme  teknikleri  hakkında  genel  bilgiler  verilerek,  veri  görselleştirmenin  önemi  üzerinde durulmuştur.

Anahtar Kelimeler:Büyük Veri, Veri Görselleştirme, Büyüklük, Çeşitlilik, Hız, Değer, Doğruluk.

The license plates system in Saudi Arabia costs millions (SAR), if not billions (SAR), but the beneciary covers most of the cost, if not all of it. In all cases, the system lacks to robustness and represents an example of impulsive creation.

Some analysts believe that Bernoulli’s utility function is “reference-independent” and hence it
is not able to generate a loss aversion index. This paper concludes otherwise. It posits that
the geometry of Bernoulli’s original utility function specification supports reference dependence
and a loss aversion index. It provides a solution to the open problem of closed form global
utility loss aversion index formula. Theory and evidence show that the formula follows a stable
law, and it supports a Fisher z-transform test for loss aversion. Higher order approximation of
Bernoulli’s specification of preferences predicts that a risk averse but temperate agent would
prefer a high kurtosis gamble to certainty equivalent if the payoff is sufficiently high. In contrast,
prospect theory predicts that no agent should prefer that gamble in gain domain. In a nutshell,
Bernoulli’s utility function is alive and well. It subsumes prospect theory’s skewed S-shape value
function for decision making under risk and uncertainty.

A new four-parameter model called the Marshall--Olkin ex\-ponential--Weibull probability distribution is being introduced in this paper, generalizing a number of known lifetime distributions. This model turns out to be quite flexible for analyzing positive data. The hazard rate functions of new model can be increasing and bathtub shaped.} Our main objectives are to obtain representations of certain statistical functions, to estimate the parameters of the proposed distribution and to discuss its modality. As an application, the probability density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson--Darling and Cram'er--von Mises goodness--of--fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.

A new four-parameter model called the gamma--exponentiated exponential--Weibull distribution is being introduced
in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain statistical
functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the
proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson--Darling and Cram\'{e}r--von Mises goodness--of--fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.

In this paper a new continuous distribution with extra two parameters called the Weibull exponentiated inverse Raleigh distribution is introduced. The new distribution based on the Weibull generated family of distributions and exponentiated inverse Raleigh distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. We investigate the shapes of the density and hazard rate function. Some statistical properties of the new distribution including moments, mean residual life, quantile and generating functions, median, skewness and kurtosis and order statistics are discussed. The estimation of the model parameters is performed by the maximum likelihood method. The importance of the new distribution is examined through real data application and the results show that the new distribution can be useful to provide better fits than other lifetime models.

Forecasting economic growth for developing countries is a problematic task, peculiarly because of particularities they face. The model identification process in this paper yielded a random walk model for the Gross Domestic Product (GDP) series. We applied ARIMA models to get empirical results and bring to a close that the models obtained are suitable for forecasting the economic output of Africa. The adequate models were used for each of 20 Africa's largest economies to forecast future time series values. Based on the estimation results, we concluded that from 1990 looking forward to 2030, there will be an increasing GDP growth where the average speed of the economy of Africa will be of 5.52%, and the GDP could achieve $2185.21 billion to $10186.18 billion.

Increasing the parameter of a distribution helps to capture the skewness and peakedness characteristic in the data sets. This allows a more realistic modeling of data arising from different real life situations. In this paper, we modified Laplace distribution using the exponentiation method. The study proved that the modified Laplace distribution (MLD) is a probability density function. Some of the basic statistical properties of the modified Laplace distribution are obtained. We applied the proposed modified Laplace distribution on two life datasets and simulated data. Parameters of the distributions were estimated using method of maximum likelihood estimation. The study compared the modified Laplace distribution with Laplace distribution and Generalized error distribution using Schwartz Criteria (SC) measure of fitness. The results obtained revealed that the modified Laplace distribution has a better fit than the Laplace and Generalized error distributions and can be used for more realistic modeling of data arising from different real life situations. The simulation results obtained shows that as the sample size increases, the Biasedness and Root Mean Square Error (RMSE) of the proposed modified Laplace distribution reduces.

Terminal based analysis software for mathematical statistics, probabilistic and data simulation models. Developed in ANSI-C for the scientific field.
The SCHRAUSSER-MAT philosophy and vision is to create and, above all, to maintain an optimally relevant and powerful tool for data analysis in the purely scientific and technical area as at universities and research institutes. 
The MAT System is divided into the areas
1) General mathematical functions, trigonometric functions and statistics
2) Linear regression and matrix calculation
3) Distribution functions
4) Probability and combinatorics
5) Randomization and data simulation models
and should contain the full range of functions corresponding to the always contemporal level of knowledge and development. This is achieved by the fact that, under the supervision of the originator to preserve the concept logic, SCHRAUSSER-MAT is open to anyone in order to expand the functions within the framework of the basic definition. This vision and approach should be retained in the long term and passed on to successors, keeping the concept original and unadulterated:
So,
no overgrowth of the system structure as the basic concept in design, ergonomics and functional definition is retained
and
it is yet permanently expandable with functions as part of the system philosophy.

Non-profit oriented and therefore freely available for everyone to use.

Dietmar Schrausser

German:
Terminal basierte Analysesoftware für Mathematische Statistik, Probabilistik und Daten Simulations Modelle. Entwickelt in ANSI-C  für den naturwissenschaftlich technischen Forschungsbereich.

In my article I discuss how likely or unlikely it was that the Ancient Greeks understood the concept of arithmetic mean because modern Greek mathematics academics certainly don't. The majority are a bunch of imbeciles who should know better.

Mainstream mathematics academia in general has never understood the meaning of an arithmetic mean. Constructing the mean is one thing, understanding it quite another. I call the arithmetic mean the second most important concept in all of mathematics, second only to that of the number concept.

I recommend that Greek academics use the expression Όρος επιπέδου (level term) rather than αριθμητικός μέσος όρος which is flawed.

Αναρωτιέμαι πόσοι από εσάς είστε πραγματικά απόγονοι Αρχαίων Ελλήνων.
Ναι, ηλίθιοι! Είστε πολλά αδαή και αμόρφωτα παπαγαλάκια.

A small excerpt from this article:

It's pretty obvious that Aristotle had trouble defining a mean and also could not have known of a well-formed definition like the one I provided earlier. So, we can dismiss his definition as vague and lacking generality. Aristotle was an anal-retentive fool in my opinion. What does the gibberish “...neither too much nor too little, and this is not one and the same for everybody...” even mean?! The arrogant dimwit Aristotle produced the first ever hand waving argument. These are common among mainstream mathematics charlatans. Some examples are: “As close as you please”; “infinitely close”; “smaller than anything you can think of”, etc. Quite ironic because Aristotle wrote screeds of garbage on interpretation and meaning. One would imagine he could have expressed himself better. Alas, this is not the case. He is also one of my least favourite philosophers. Aristotle was not a mathematician.

Eventology of multivariate statistics
Eventology and mathematical eventology
Philosophical eventology and philosophy of probability
Practical eventology
Eventology of safety
Eventological economics and psychology
Mathematics in the humanities, socio-economic and natural sciences
Financial and actuarial mathematics
Multivariate statistical analysis
Multivariate complex analysis
Decision-making under risk and uncertainty
Risk measurement and risk models
Theory of fuzzy events and generalized theory of uncertainty
System analysis and events management

EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem

With topics from quantum physics, probability and believability to economics, sociology, and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts, and ideas on the axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem.
Eventology of experience and chance
Believability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance

A new generalized extended inverse Gaussian density function involving a confluent hypergeometric function is defined. Closed form representations of a generalized extended inverse Gaussian density function and the corresponding moment generating function are provided in terms of Meijer’s G-function. Some other statistical functions which are associated with the proposed distribution are also derived. Many distributions can be obtained as limiting cases of the proposed density function. This density is utilized to model an actual data set. The new distribution provides a better fit than related distributions as measured by the Anderson-Darling and Cramér-von Mises statistics. The proposed distribution could, for instance, find applications in the physical and biological
sciences and in particular be helpful to researchers working in special functions as well as reliability analysis, survival models and diffraction theory.

We exist in the world of uncertainties.
Any uncertainty always arises from a conflict of experience and chance, more precisely, from a conflict between the observer's experience and the chance observation. In other words, this indivisible pair, ``experience and chance'', is the source of any uncertainty.
Other sources of uncertainty simply do not exist.
A theory that describes this conflict strictly mathematically is the new theory, called theory of co~events, or the theory of experience and chance. Now we can say that this theory is a theory of uncertainty in its broadest sense.

The eventology approach gave impetus to the development of a theory that turned out to be broader than the theory of probabilities.
This new theory is a dual combination of two theories - Kolmogorov's theory of probabilities of ket-events (k-e.'s) and its dual reflection - a new theory of believabilities of bra-events (b-e.'s). Today, the theory of co~events has a strict axiomatics, in which Kolmogorov k-e.'s describing the future case of observation are dually reflected in b-e.'s describing the past experience of the observer, and a co~event is defined as a measurable binary relation on the Cartesian product: ``a set of bra-events X a set of terraced ket-events''.

Goodness of fit test is a test that has attracted researchers’ interest over the decades. This study is
on goodness of fit test for normal distribution only. The Kolmogorov-Smirnov (K-St) and Pearson’s
Chi-square (χ² test) goodness of fit test were used to determine the normality of a given data. The
result revealed that the data is normal under the two tests and that the Kolmogorov-Smirnov (K-S
test) were preferred to Pearson’s Chi-square (χ² test). The Kolmogorov-Smirnov (K-S) test of
goodness of fit is the most suitable in terms of the p-value.

In this article, a new four-parameter lifetime model named the Weibull quasi Lindley distribution based on the Weibull G-family is introduced. It is more flexible than several recently introduced lifetime distributions. Various structural properties of the new distribution are derived including moments, moment generating function, quantile function, reliability, hazard rate function and mean residual life. Expressions for the R´enyi, q-entropies and density function of order statistics are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. Two real data sets are presented to illustrate the advantage of the new distribution. In fact, the new model provides a better fit to this data than some of the most important distributions.

The book about the eventology ~ a science about events and its applications to problems of management of sets of events ~ a new direction in philosophy, mathematics and event management (see English version of the book: https://www.academia.edu/38605343/).
This book outlines ideas that inspired me while I was trying to build a new event science, eventology. Not each of these ideas was developed, but all of them inspired me in the construction of eventology, and then in the discovery of a revolutionary theory of experience and chance, co~eventum mechanics. (see, for example, https://www.academia.edu/34357251,
https://www.academia.edu/34373279,
https://www.academia.edu/34390291,
https://www.academia.edu/38368776,
https://www.academia.edu/38154263 and so on).