Benfords Law or the First Digit Law Essay Example | Topics and Well Written Essays - 1000 words

Benfords Law or the First Digit Law - Essay Example I can astronomer names Simon Newcomb, who noticed that the earlier pages of logarithm tables that are used in the performance of calculations were much more worn than other pages. Newcomb published result become the first known instance of this observation and also includes the distribution of the second digit. He then proposed a law that is based on the probability of a single number N that is the first digit of a number was equal to log(N  +  1)  Ã¢Ë†â€™Ã‚  log(N). The results from Benford’s law are used in different data such as street addresses, electricity bills, population numbers, lengths or rivers, stock prices, death rates, mathematical and physical constants as well as processes that are described using power law. The main condition for this law is that the data set or population must only consist of natural numbers (Nigrini 170). The results from the law tend to be highly accurate whenever the values are distributed across numerous orders of magnitude. Benford’s law is also highly used in the detection of fraud, errors, embezzlements, and sloppy accountants. This is because those people who normally commit a crime may end up creating fake payment amounts that may appear real. Benford’s law is a data mining approach that is used in auditing in order to examine the digit properties in different accounting data for the purposes of character identification. However, unless the person committing is aware of Benford’s law of distribution, then he will not be in a position to make up numbers that follow the proper curve and this makes it very easy to spot a potential fraud. People who commit a crime also tend to distribute their digits in a fairly uniform manner. With a simple comparison of the frequency of the first digit from the data in accordance with the expected distributing according to Benford’s law will always reveal anomalous results. Based on this idea, Benford’s law could be used in auditing and forensic auditing to act as an indicator.

Critical Thinking Essay Example | Topics and Well Written Essays - 750 words - 14

Critical Thinking - Essay Example As shown below these three sources are of greatest threat to our well-being. Motor vehicles have been pointed out as a major source of environmental pollution for a long time; they produce CO2 among other poisonous gases, which are responsible for the depletion of the ozone layer as well as CO, which is a non-detectable poisonous gas. Coal, which is also burned in several industries as a source of energy, has been flagged by environmentalists as a major contributor to carbon dioxide too. Other sources of pollutants include fossil fuels which act as a source of Sulfur Dioxide when burnt and Nitrogen Oxide which is produced when the fuels in vehicles are combusted (Sukhraj 18). Air pollutants have been shown to have several detrimental effects to the environment. The gases interact with the water in the atmosphere to produce acidic rain, which is corrosive and therefore erodes the paint of buildings and kills life in plants and rivers due to its poisonous nature. These fumes have also been identified as carcinogenic and over time, residents living in places with high pollution rates will have a higher prevalence rate of eyes nose and throat infections as well as the development of cancer. There reduction of air pollution is very important and several steps have been taken to do this. Vehicles have been given several standards of performance, which all companies must maintain failure to which their vehicles will not be allowed in certain countries. Catalytic converters have also been installed in vehicles and in factories where sulfur is a by-product so as to reduce the sulfur compounds released into the environment (Sukhraj 23). The introduction of harmful substances to soil and water is another problem that is being faced in many places. Most water pollutants are manmade and are a result of industrial activity too close to agricultural land and water sources. However, natural sources of water pollution include water