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Bass Diffusion Model
The Bass model or Bass diffusion model was developed by Frank Bass. It consists of a simple differential equation that describes the process of how new products get adopted in a population. The model presents a rationale of how current adopters and potential adopters of a new product interact. The basic premise of the model is that adopters can be classified as innovators or as imitators and the speed and timing of adoption depends on their degree of innovation and the degree of imitation among adopters. The Bass model has been widely used in forecasting, especially new products' sales forecasting and technology forecasting. Mathematically, the basic Bass diffusion is a Riccati equation with constant coefficients equivalent to Verhulst--Pearl Logistic growth. In 1969, Frank Bass published his paper on a new product growth model for consumer durables. Prior to this, Everett Rogers published ''Diffusion of Innovations'', a highly influential work that described the different st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Bass
Frank M. Bass (December 27, 1926 – December 1, 2006) was an American academic in the field of marketing research and marketing science. He was the creator of the Bass diffusion model that describes the adoption of new products and technologies by first-time buyers. He died on December 1, 2006. Career Bass grew up in the small town of Cuero, Texas. He served in the United States Navy for two years (1944–46). He received his BBA from Southwestern University in 1949, and his MBA from the University of Texas in 1950. After completing his M.B.A. at Texas, he became interested in marketing issues. He worked as a teaching assistant and assistant professor in marketing while earning his Ph.D. at the University of Illinois in 1954. In 1957 he became an assistant professor in marketing at the University of Texas. In 1959, Bass was made a Fellow at Harvard University's Institute of Basic Mathematics For Application to Business. This exposure to advanced analytic methods influenced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Innovation
Innovation is the practical implementation of ideas that result in the introduction of new goods or services or improvement in offering goods or services. ISO TC 279 in the standard ISO 56000:2020 defines innovation as "a new or changed entity realizing or redistributing value". Others have different definitions; a common element in the definitions is a focus on newness, improvement, and spread of ideas or technologies. Innovation often takes place through the development of more-effective products, processes, services, technologies, art works or business models that innovators make available to markets, governments and society. Innovation is related to, but not the same as, invention: innovation is more apt to involve the practical implementation of an invention (i.e. new / improved ability) to make a meaningful impact in a market or society, and not all innovations require a new invention. Technical innovation often manifests itself via the engineering process when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shifted Gompertz Distribution
The shifted Gompertz distribution is the distribution of the larger of two independent random variables one of which has an exponential distribution with parameter b and the other has a Gumbel distribution with parameters \eta and b . In its original formulation the distribution was expressed referring to the Gompertz distribution instead of the Gumbel distribution but, since the Gompertz distribution is a reverted Gumbel distribution, the labelling can be considered as accurate. It has been used as a model of Diffusion of innovations, adoption of innovations. It was proposed by Bemmaor (1994). Some of its statistical properties have been studied further by Jiménez and Jodrá (2009) and Jiménez Torres (2014). It has been used to predict the growth and decline of social networks and on-line services and shown to be superior to the Bass model and Weibull distribution (Bauckhage and Kristian Kersting, Kersting 2014). Specification Probability density function The probabilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lazy User Model
The lazy user model of solution selection (LUM) is a model in information systems proposed by Tétard and Collan that tries to explain how an individual selects a solution to fulfill a need from a set of possible solution alternatives. LUM expects that a solution is selected from a set of available solutions based on the amount of effort the solutions require from the user – the user is supposed to select the solution that carries the least effort. The model is applicable to a number of different types of situations, but it can be said to be closely related to technology acceptance models. The model draws from earlier works on how least effort affects human behaviour in information seeking and in scaling of language. Earlier research within the discipline of information systems especially within the topic of technology acceptance and technology adoption is closely related to the lazy user model. The model structure The model starts from the observation that there is a " user ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forecasting
Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself. Usage can vary between areas of application: for example, in hydrology the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction; it is generally considered a good practice to indicate the degree of uncertainty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion Of Innovation
Diffusion of innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread. Everett Rogers, a professor of communication studies, popularized the theory in his book ''Diffusion of Innovations''; the book was first published in 1962, and is now in its fifth edition (2003). Rogers argues that diffusion is the process by which an innovation is communicated over time among the participants in a social system. The origins of the diffusion of innovations theory are varied and span multiple disciplines. Rogers proposes that five main elements influence the spread of a new idea: the innovation itself, adopters, communication channels, time, and a social system. This process relies heavily on social capital. The innovation must be widely adopted in order to self-sustain. Within the rate of adoption, there is a point at which an innovation reaches critical mass. In 1989, management consultants working at the consulting firm Regis Mckenna Inc. the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Communities
A virtual community is a social network of individuals who connect through specific social media, potentially crossing geographical and political boundaries in order to pursue mutual interests or goals. Some of the most pervasive virtual communities are online communities operating under social networking services. Howard Rheingold discussed virtual communities in his book, ''The Virtual Community'', published in 1993. The book's discussion ranges from Rheingold's adventures on The WELL, computer-mediated communication, social groups and information science. Technologies cited include Usenet, MUDs (Multi-User Dungeon) and their derivatives MUSHes and MOOs, Internet Relay Chat (IRC), chat rooms and electronic mailing lists. Rheingold also points out the potential benefits for personal psychological well-being, as well as for society at large, of belonging to a virtual community. At the same time, it showed that job engagement positively influences virtual communities of practic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shifted Gompertz Distribution
The shifted Gompertz distribution is the distribution of the larger of two independent random variables one of which has an exponential distribution with parameter b and the other has a Gumbel distribution with parameters \eta and b . In its original formulation the distribution was expressed referring to the Gompertz distribution instead of the Gumbel distribution but, since the Gompertz distribution is a reverted Gumbel distribution, the labelling can be considered as accurate. It has been used as a model of Diffusion of innovations, adoption of innovations. It was proposed by Bemmaor (1994). Some of its statistical properties have been studied further by Jiménez and Jodrá (2009) and Jiménez Torres (2014). It has been used to predict the growth and decline of social networks and on-line services and shown to be superior to the Bass model and Weibull distribution (Bauckhage and Kristian Kersting, Kersting 2014). Specification Probability density function The probabilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Distribution
Logistic may refer to: Mathematics * Logistic function, a sigmoid function used in many fields ** Logistic map, a recurrence relation that sometimes exhibits chaos ** Logistic regression, a statistical model using the logistic function ** Logit, the inverse of the logistic function ** Logistic distribution, the derivative of the logistic function, a continuous probability distribution, used in probability theory and statistics * Mathematical logic, subfield of mathematics exploring the applications of formal logic to mathematics Other uses * Logistics, the management of resources and their distributions ** Logistic engineering, the scientific study of logistics ** Military logistics Military logistics is the discipline of planning and carrying out the movement, supply, and maintenance of military forces. In its most comprehensive sense, it is those aspects or military operations that deal with: * Design, development, acqui ..., the study of logistics at the service of milit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions. Definitions Probability density function The probability density function (pdf) of an exponential distribution is : f(x;\lambda) = \begin \lam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
